No CrossRef data available.
Article contents
Roland L. Dobrushin (1929–1995)
Published online by Cambridge University Press: 14 October 2010
Abstract
An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Information
- Type
- Obituary
- Information
- Copyright
- Copyright © Cambridge University Press 1996
References
Publications
[1]On regularity conditions for time-homogeneous Markov processes with countable set of possible states. Usp. Mat. Nauk 7 (1952), 185–191.Google Scholar
[2]A generalization of the Kolmogorov equations for Markov processes with a finite number of possible states. Mat. Sbornik 33 (1953), 567–596.Google Scholar
[3]A limit theorem for Markov chains with two states. Izv. Sov. Acad. Sci., Ser. Math. 17 (1953), 291–330. (Engl. Transl: Select. Transl. Math. Stat. Prob. 1 (1961), 97–196 (Inst. Math. Stat. and Amer. Math. Soc.)).Google Scholar
[4]Conditions of regularity for Markov processes with a finite number of possible states. Mat. Sborn. 34 (1954), 541–556.Google Scholar
[5]A lemma on the limit of a superposition of random functions. Usp. Mat. Nauk 10 (1955), 157–159.Google Scholar
[6]Two limit theorems for the simplest random walk on a line. Usp. Mat. Nauk 10 (1955), 139–146.Google Scholar
[7]Central limit theorem for non-homogeneous Markov chains. Rep. Sov. Acad. Sci. 102 (1955), 5–8.Google Scholar
[8]On conditions for the central limit theorem for non-homogeneous Markov chains. Rep. Sov. Acad. Sci. 108 (1956), 1004–1006.Google Scholar
[9]Central limit theorem for non-homogeneous Markov chains I. Theor. Prob. Appl. 1 (1956), 72–89. (Engl. Transl: 1 (1956), 65–80.)Google Scholar
[10]Central limit theorem for non-homogeneous Markov chains II. Theor. Prob. Appl. 1 (1956), 365–425. (Engl. Transl: 1 (1956), 291–330.)Google Scholar
[11]An example of a countable homogeneous Markov chain, all states of which are instantaneous. Theor. Prob. Appl. 1 (1956), 481–485.Google Scholar
[12]On the Poisson law for the distribution of particles in space. Ukrain. Math. J. 8 (1956), 130–134.Google Scholar
[13](With Jaglom, A..) Complement to the Russian translation of the book: J. 1. Doob. Stochastic Processes. 1956, p. 576–688.Google Scholar
[14]Some classes of homogeneous countable Markov processes. Theor. Prob. Appl. 2 (1957).Google Scholar
[15]A statistical problem in signal detecting theory for a multi-channel system reducing to stable distribution laws. Theor. Prob. Appl. 3 (1957), 173–185.Google Scholar
[16]Transmission of information in channels with feedback. Theor. Prob. Appl. 3 (1957), 395–412.Google Scholar
[17]A simplified method of experimental evaluation of the entropy of stationary sequences. Theor. Prob. Appl. 3 (1957), 462–464.Google Scholar
[18]A general formulation of the basic Shannon theorem in information theory. Rep. Soc. Acad. Sci. 126 (1959), 474–477.Google Scholar
[19]A general formulation of the basic Shannon theorem in information theory. Usp. Math. Nauk 14 (1959), 3–103. (Engl. Transl: Amer. Math. Soc. Transl. 2 (1959), 323–438. There also exists Chinese, Czech, German and Hungarian translations.)Google Scholar
[20]Optimal transmission of information in a channel with unknown parameters. Radiotechnol. and Electron. 4 (1959), 1951–1956.Google Scholar
[21]Limit approach under the signs of information and entropy. Theor. Prob. Appl. 5 (1960), 29–37.Google Scholar
[22]Properties of sample functions of stationary Gaussian processes. Theor. Prob. Appl. 5 (1960), 132–134.Google Scholar
[23]Asymptotics of the error probabilities for the transmission of information in memoryless channels with symmetric matrix of transaction probabilities. Rep. Sov. Acad. Sci. 133 (1960), 265–268.Google Scholar
[24](With Hurgin, J. and Tsybakov, B..) An approximate computation of the capacity of radio channels with random parameters. Proc. Soviet meeting on Theor. Prob., Math. Stat. (Erevan, 1960). 1960, pp. 164–171.Google Scholar
[25](With Jaglom, A. and Jaglom, I..) Theory of information and linguistics. Problems of Linguistics 1 (1960), 10–110.Google Scholar
[26]Mathematical methods in linguistics. Math. Education. 1961. (There also exist Czech and Polish translations.)Google Scholar
[27]Mathematical problems in the Shannon theory of optimal coding of information. Proc. Fourth Berkeley Symp. Math. Stat. and Prob. University of California Press, 1961, pp. 211–252.Google Scholar
[28]Optimal binary codes for small rates of information transmission. Theor. Prob. Appl. 7 (1962), 208–213.Google Scholar
[29]Asymptotic estimates of the error probability for transmission of messages through a discrete memoryless communication channel with a symmeric matrix of transaction probabilities. Theor. Prob. Appl. 7 (1962), 283–311.Google Scholar
[30]Asymptotic estimates of the error probabilities for the transmission of messages through memoryless channels with a feed-back. Probl. Cybernetics 8 (1962), 161–168.Google Scholar
[31](With Tsybakov, B..) Information transmission with additional noise. IEEE Trans. Inform. Theory 8 (1962), 293–304.Google Scholar
[32]Asymptotic optimality of group and systematic codes for some channels. Theor. Prob. Appl. 8 (1963), 52–66.Google Scholar
[33]Unified methods of information transmission for discrete memoryless channels and messages with independent components. Rep. Sov. Acad. Sci. 148 (1963), 1245–1248.Google Scholar
[34]Unified methods of information transmission: a general case. Rep. Sov. Acad. Sci. 149 (1963), 16–19.Google Scholar
[35](With Pinsker, M. and Shiryaev, A..) An application of the entropy to problems of signal detecting against a background of noise. Litov. Mat. Shorn. 3 (1963), 107–122.Google Scholar
[36]Possibilities of applications of limit theorems of probability theory to some physical problems. Limit Theorems of Probability Theory. Tashkent, 1963, pp. 15–37.Google Scholar
[37]On the Wozencraft-Reiffen method of sequential decoding. Probl. Cybernetics 12 (1964), 113–123.Google Scholar
[38]Investigation of conditions for asymptotical existence of the configurational integral for the Gibbs distribution. Theor. Prob. Appl. 9 (1964), 626–643.Google Scholar
[39]Methods of probability theory in statistical physics. Winter School Theor. Prob. Mat. Stat. (Uzgorod). 1964, pp. 221–263.Google Scholar
[40]Existence of a phase transition in the two-dimensional Ising models. Rep. Sov. Acad. Sci. 160 (1965), 1046–1048.Google Scholar
[41]Existence of a phase transition in the two-dimensional and three-dimensional Ising models. Theor. Prob. Appl. 10 (1965), 209–230.Google Scholar
[42]Existence of phase transitions in models of a lattice gas. Proc. Fifth Berkeley Symp. Math. Stat. and Prob., vol. 3. University of California Press, 1966, pp. 73–87.Google Scholar
[44](With Minlos, R..) Existence and continuity of the pressure in classical statistical physics. Theor. Prob. Appl. 12 (1967), 595–618.Google Scholar
[45]Shannon theorems for channels with synchronization errors. Prob. Inform. Transm. 3 (1967), 8–36.Google Scholar
[46]Description of a random field by means of conditional probabilities and conditions of its regularity. Theor. Prob. Appl. 13 (1968), 201–229.Google Scholar
[47]Gibbsian random fields for lattice systems with pair interactions. Fund. Anal. Appl. 2 (1968), 31–43.Google Scholar
[48]Problem of the uniqueness of a Gibbsian random field and problem of phase transitions. Fund. Anal. Appl. 2 (1968), 44–57.Google Scholar
[49](With Vvedenskaja, N..) Calculation on a computer of the capacity of communication channels with exclusion of symbols. Probl. Inform. Transm. 4 (1968), 92–95.Google Scholar
[51](With Pjatetskii-Shapiro, I. and Vasiljev, N..) Markov processes on the infinite product of discrete spaces. Soviet-Japanese Symp. Prob. Theory (Khabarovsk). 1969, pp. 3–29.Google Scholar
[52](With Pinsker, M..) Memory increases capacity. Probl. lnformJransm. 5 (1969), 94–95.Google Scholar
[53]Gibbsian random fields for particles without hard core. Theor. Mat. Phys. 4 (1970), 101–118.Google Scholar
[54]Description of a system of random variables by means of conditional distributions. Theor. Prob. Appl. 15 (1970), 469–497.Google Scholar
[55]Unified methods of optimal quantization of messages. Probl. Cybernetics 22 (1970), 107–157.Google Scholar
[56]Markov processes with a large number of locally interacting components: existence of a limit processes and their ergodicity. Probl. Inform. Transm. 7 (1971), 70–87.Google Scholar
[57]Markov processes with many locally interacting components—the reversible case and some generalizations. Probl. Inform. Transm. 7 (1971), 57–66.Google Scholar
[58](With Minlos, R. and Suhov, Yu..) Review of some recent results. Complement to the Russian translation of the book: D. Ruelle. Statistical Mechanics. Rigorous Results. 1971, pp. 314–361.Google Scholar
[59]Asymptotical behaviour of Gibbsian distributions in dependence on a form of a volume. Theor. Math. Phys. 12 (1972), 115–134.Google Scholar
[60]A Gibbsian state describing a coexistence of phases for the three-dimensional Ising model. Theor. Prob. Appl. 17 (1972), 619–639. (Reprinted in Mathematical Problems of Statistical Mechanics. World Scientific, 1991.)Google Scholar
[61](With Gelfand, S..) Complexity of asymptotically optimal code realization by constant depth schemes. Prob. Control Info. Theor. 1 (1972), 197–215.Google Scholar
[62]Survey of Soviet research in information theory. Trans. IEEE, Sect. Inf. Theor. 18 (1972), 703–724.CrossRefGoogle Scholar
[63]An investigation of Gibbsian states for three-dimensional lattice systems. Theor. Prob. Appl. 18 (1973), 261–279. (Reprinted in Mathematical Problems of Statistical Mechanics. World Scientific, 1991.)Google Scholar
[64]Analyticity of correlation function in one-dimensional classical systems with slowly decreasing potentials. Comm. Math. Phys. 32 (1973), 269–289.CrossRefGoogle Scholar
[65](With Minlos, R..) Construction of one-dimensional quantum field with the help of a continuous Markov field. Funct. Anal. Appl. 7 (1973), 81–82.Google Scholar
[66]Mathematization of linguistics. Izv. Sov. Acad. Sci., Ser. Literat., Linguist. 32 (5) (1973).Google Scholar
[67](With Gelfand, S. and Pinsker, M..) On complexity of coding. Proc. Second Intern. Symp. on Inform. Theory (Zahkadzor, Armenia). Academiai Kiado, Budapest, 1973, pp. 177–184.Google Scholar
[68]Conditions of absence of phase transitions in one-dimensional classical systems. Mat. Shorn. 93 (1974), 29–49.Google Scholar
[69]Analyticity of correlation functions in one-dimensional classical systems with a slowly power decrease of potential. Mat. Shorn. 94 (1974), 16–48.Google Scholar
[70](With Gerzik, V..) Gibbsian states in a lattice model with the interaction on two steps. Fund. Anal. Appl. 8 (1974), 12–25.Google Scholar
[71](With Nakhapetjan, B..) Strong convexity of the pressure for lattice systems of classical statistical physics. Theor. Mat. Phys. 20 (1974), 223–234.Google Scholar
[72](With Shlosman, S..) Absence of breakdown of continuous symmetry in two-dimensional models of statistical physics. Comm. Math. Phys. 42 (1975), 31–40.Google Scholar
[73](With Pirogov, S..) Theory of random fields. Proc. IEEE-USSR Joint Workshop on Information Theory. Moscow, IEEE Service Center, 1975Google Scholar
[74](With Stambler, S..) Coding theorems for some classes of arbitrary varying discrete memoryless channels. Probl. Inform. Transm. 11 (1975), 2–22.Google Scholar
[75](With Minlos, R..) Factor measures on measurable spaces. Proc. Moscow Math. Soc. 32 (1975), 77–92.Google Scholar
[76](With Minlos, R..) An investigation of properties of generalized Gaussian random fields. Problems of Mechanics and Mathematical Physics. Moscow, 1976, pp. 117–165. (Engl. transl: Sel. Math. Soc. 1 (1980, 215–263.)Google Scholar
[77](With Suhov, Yu..) Asymptotical investigation of starlike message switching networks with a large number of radial rays. Probl. Inform. Transm. 12 (1976), 70–94.Google Scholar
[78](With Tirozzi, B..) The central limit theorem and the problem of equivalence of ensembles. Comm. Math. Phys. 54 (1977), 173–192.Google Scholar
[79](With Fritz, J..) Nonequilibrium dynamics of one-dimensional infinite particle systems with a singular interaction. Comm. Math. Phys. 55 (1977), 275–292.Google Scholar
[80](With Fritz, J.). Nonequilibrium dynamics of two-dimensional infinite particle systems with a singular interaction. Comm. Math. Phys. 57 (1977), 67–81.CrossRefGoogle Scholar
[81](With Minlos, R..) Polynoms of linear random functions. Usp. Mat. Nauk (Russ. Math. Surveys) 32 (1977), 67–122.Google Scholar
[82](With Ortjukov, S..) On a lower estimate of the redundancy of self-correcting schemes with unreliable functional elements. Probl. Inform. Transm. 13 (1977), 83–89.Google Scholar
[83](With Ortjukov, S..) An upper estimate of the redundancy of self-correcting schemes with unreliable functional elements. Probl. Inform. Transm. 13 (1977), 56–76.Google Scholar
[84]Automodel generalized random fields and their renorm-groups. Multicomponent Random Systems. Nauka, Moscow, 1978, pp. 179–213. (Engl. transl: Advances in Probability 5. Marcel Dekker, New York and Basel, 1980, pp. 153–198.)Google Scholar
[85](With Shlosman, S..) Nonexistence of one and two-dimensional Gibbs fields with a noncompact group of continuous symmetries. Multicomponent Random Systems. Nauka, Moscow, 1978, pp. 214–223. (Engl. transl: Advances in Probability 5. Marcel Dekker, New York and Basel, 1980, pp. 199–210).Google Scholar
[86](With Suhov, Yu..) On the problem of the mathematical foundation of the Gibbs postulate in classical statistical mechanics. Led. Notes Phys. 80 (1978), 325–340.Google Scholar
[87](With Minlos, R..) Polynomials of a generalized random field and its moments. Theor. Prob. Appl. 23 (1978), 715–730.Google Scholar
[88]Gaussian and their subordinated self-similar random generalized fields. Ann. Prob. 7 (1979), 1–28.Google Scholar
[89](With Major, P..) Non-central limit theorems for nonlinear functions of Gaussian fields. Z. Wahrsch. Verw. Ceb. 50 (1979), 27–52.Google Scholar
[91](With Suhov, Yu..) Time asymptotics for some degenerate models of time evolution for system with infinite number of particles. Modern Probl. of Math. 14 (1979), 147–254.Google Scholar
[92](With Surgailis, D..) On the innovation problem for Gaussian Markov random fieds. Z Wahrsch. Verw. Geb. 49 (1979), 275–291.Google Scholar
[93](With Prelov, V..) Asymptotic approach to the investigation of message switching networks of a linear structure with a large number of nodes. Probl. Inform. Transm. 15 (1979), 61–73.Google Scholar
[94]Gaussian random fields—Gibbsian point of view. Multicomponent Random Systems. Marcel Dekker, New York and Basel, 1980, pp. 119–152.Google Scholar
[95](With Sinai, Ya..) Mathematical problems in statistical mechanics. Sov. Sci. Rev. Sel. C, Math. Phys. Rev., vol 1. Harwood, 1980, pp. 55–106.Google Scholar
[96](With Boldrighini, C. and Suhov, Yu..) Hydrodynamical limit for a degenerate model of classical statistical mechanics. Usp. Mat. Nauk 35 (1980), 152.Google Scholar
[97](With Pechersky, E..) Uniqueness conditions for finitely dependent random fields. Random Fields, vol. 1, Coll. Math. Soc. Janos Bolyai, 27. North-Holland, 1981, 223–262.Google Scholar
[98](With Shlosman, S..) Phases corresponding to minima of the local energy. Selecta Math. Sov. 1 (1981), 317–338.Google Scholar
[99](With Major, P..) On asymptotical behavior of some self-similar random fields. Selecta Math. Sov. 1 (1981), 265–291.Google Scholar
[100](With Gray, R. M. and Ornstein, D. S..) Block synchronization, sliding-block coding, invulnerable sources and zero error codes for discrete noisy channels. Ann. Prob. 8 (1981), 639–674.Google Scholar
[101](With Pechersky, E..) A criterion of the uniqueness of Gibbsian fields in the non-compact case. Led. Notes in Math. 1021 (1982), 97–110.Google Scholar
[102](With Siegmund-Schultze, R..) The hydrodynamic limit for systems of particles with independent evolution. Math. Nachr. 105 (1982), 199–204.Google Scholar
[103]Hydrodynamic limit approach: some caricatures. Interacting Markov Processes and Their Application to Mathematical Modelling of Biological Systems. Putshino, 1982, pp. 7–20.Google Scholar
[104](With Boldrighini, C. and Suhov, Yu..) One dimensional hard rod caricature of hydrodynamics. J. Stat. Phys. 31 (1983), 577–615.CrossRefGoogle Scholar
[105](With Kelbert, M..) Local additive functionals of Gaussian random fields. Theor. Prob. Appl. 28 (1983), 32–44.Google Scholar
[106](With Kelbert, M..) Stationary local additive functionals of Gaussian fields. Theor. Prob. Appl. 28 (1983), 489–503.Google Scholar
[107](With Shlosman, S..) Constructive criterion for the uniqueness of Gibbs fields. Stat. Phys. And Dynamical systems. Rigorous results (Progr. in Phys. 10). Birkhauser, 1985, pp. 347–370.Google Scholar
[108](With Shlosman, S..) Completely analytical Gibbs fields. Stat. Phys. and Dynamical systems. Rigorous results (Progr. in Phys. 10). Birkhauser, 1985, pp. 371–404.Google Scholar
[109](With Kolafa, I. and Shlosman, S..) Phase diagram of the two-dimensional Ising antiferromagnet. Comm. Math. Phys. 102 (1985), 81–103.Google Scholar
[110](With Avetisjan, M..) A condition of the linear regularity for vector random fields. Probl. Inform. Transm. 21 (1985), 76–82.Google Scholar
[111](With Shlosman, S..) The problem of translation invariance of Gibbs states at low temperature. Soviet Sci. Rev., Sect. Math. Phys. Rev., vol. 5. Harwood, 1985, pp. 53–195.Google Scholar
[112](With Sinai, Ya. and Suhov, Yu..) Dynamical systems of statistical mechanics. Modern Problems of Math., Fundament. Direct., vol. 2. 1985, pp. 235–284.Google Scholar
[113](With Zahradnik, M..) Phase diagrams for continuous-spin models. An extension of the Pirogov-Sinai theory. Mathematical Problems of Statistical Mechanics and Dynamics. Reidel, 1986, pp. 1–124.Google Scholar
[114](With Bassalygo, L..) Uniqueness of a Gibbs field with a random potential—an elementary approach. Theor. Prob. Appl. 31 1986, 651–670.Google Scholar
[115](With Pellegrinotti, A., Suhov, Yu. and Triolo, L..) One-dimensional harmonic lattice caricature of hydrodynamics. J. Stat. Phys. 43 (1986), 571–608.Google Scholar
[116](With Shlosman, S..) Completely analytical interactions: constructive description. J. Stat. Phys. 46 (1987), 983–1014.Google Scholar
[117]Induction on volume and no cluster expansion. Proc. Viiith Int. Cong, on Math Phys. Eds Mebkhout, M. and Seneor, B.. World scientific, Singapore, 1987, pp. 73–91.Google Scholar
[118](With Bassalygo, L..) Epsilon entropy of Gibbsian fields. Probl. Inform. Transm. 23 (1987), 3–15.Google Scholar
[119]Theory of information. Comments and complements to: A. N. Kolmogorov. Theory of Information and Theory of Algorithms. Nauka, 1987, pp. 254–257.Google Scholar
[120]A new approach to the analysis of Gibbs perturbations of Gaussian fields. Selecta Math. Sov. 7 (1988), 221–277.Google Scholar
[121](With Martirosjan, M..) Non-finite perturbation of Gibbsian fields. Theor. and Math. Phys. 74 (1988), 10–20.Google Scholar
[122](With Martirosjan, M..) A possibility of high-temperture phase transition due to many-particle character of potential. Theor. Math. Phys. 75 (1988), 443–448.Google Scholar
[123](With Pelegrinotti, A., Suhov, Yu. and Triolo, L..) One-dimensional harmonic lattice carricature of hydrodynamics: second approximation. J. Stat. Phys. 52 (1988), 423–439.Google Scholar
[124](With Fritz, J. and Suhov, Yu..) A. N. Kolmogorov—Founder of the theory of reversible Markov processes. Usp. Mat. Nauk (Runs. Math. Surveys) 43 (1988), 157–182.Google Scholar
[125]Caricatures of Hydrodynamics. Proc. IX Int. Cong. Math. Phys. Adam Hilger, Bristol, 1989, pp. 117–132.Google Scholar
[126](With Kotecky, R. and Shlosman, S..) Equilibrium crystal shapes—a microscopic proof of the Wulff construction. Proc. XXIVth Karpacz Winter School, Stochastic Meth. in Math. Phys. World Scientific, 1989, pp. 221–229.Google Scholar
[127](With Kelbert, M., Rybko, A. and Shove, X..) Qualitative methods of queuing network theory. Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis. Eds Dobrushin, R., Kryukov, V. and Toom, A.. Manchester University Press, 1990, pp. 183–224.Google Scholar
[128](With Sokolovskii, F..) Higher order hydrodynamic equations for a system of independent random walks. Random walks, Brownian Motion and Interacting Particle Systems. A Festschrift in Honor of Frank Spitzer. Eds Durret, R. and Kesten, H.. Birkhauser, Boston-Basel-Berlin, 1991, pp. 231–254.Google Scholar
[129](With Kotecky, R. and Shlosman, S..) Wulff Construction: A Global Shape From Local Interaction. American Mathematical Society, 1992, p. 235Google Scholar
[130](With Shlosman, S..) Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction. Ideas and Methods in Mathematical Analysis, Stochastics and Application, vol. 2. Cambridge University Press (in Print).Google Scholar
[131](With Shlosman, S..) Large deviations behavior of statistical mechanics models in multi phase regime. Mathematical Physics 10 (Proceedings, Leipzig, Germany). 1991, pp. 328–333.CrossRefGoogle Scholar
[132]A formula of full semi-invariants. Cellular Automata and Cooperation Systems. Eds Boccara, N., Goles, E., Martiner, S. and Picco, P.. Kluwer, Dodrecht-Boston-London, 1993, pp. 135–140.CrossRefGoogle Scholar
[133](With Kusuoka, S..) On the way to the mathematical foundations of statistical mechanics. Statistical Mechanics and Fractals (Lecture Notes in Math. 1567). Springer, 1993, pp. 1–37.Google Scholar
[134]A statistical behaviour of shapes of boundaries of phases. Phase Transitions: Mathematics, Physics, Biology … Ed. Kotecky, R.. 1993, pp. 60–70Google Scholar
You have
Access