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Ergodic properties of a gas of one-dimensional hard rods with an infinite number of degrees of freedom. (English. Russian original) Zbl 0257.60036
Funct. Anal. Appl. 6, 35-43 (1972); translation from Funkts. Anal. Prilozh. 6, No. 1, 41-50 (1972).

60K35 Interacting random processes; statistical mechanics type models; percolation theory
37A60 Dynamical aspects of statistical mechanics
Full Text: DOI
[1] K. L. Volkovysskii and Ya. G. Sinai, ”Ergodic properties of an ideal gas with an infinite number of degrees of freedom,” Funkts. Analiz.,5, No. 4, 19-21 (1971). · Zbl 0307.76005
[2] A. N. Kolmogorov, ”A new metric invariant of transitive automorphisms and flows of Lebesgue spaces,” Dokl. Akad. Nauk SSSR,119, No. 5, 861-864 (1958). · Zbl 0083.10602
[3] V. A. Rokhlin, ”New progress in the theory of transformations with invariant measure,” Uspekhi Mat. Nauk,15, No. 4, 3-26 (1960). · Zbl 0102.33001
[4] Ya. G. Sinai, ”Probabilistic ideas in ergodic theory,” Proc. Intern. Math. Congress, Stockholm, 540-559 (1963). · Zbl 0127.33403
[5] N. N. Bogolyubov, Problems of Dynamical Theory in Statistical Physics, Gostekhizdat, Moscow (1946). · Zbl 0063.00497
[6] J. Uhlenbeck and J. Ford, Lectures on Statistical Mechanics [Russian translation], Mir, Moscow (1965).
[7] D. W. Jepsen, ”Dynamics of a simple many-body system of hard rods,” J. Math. Phys.,6, 405-414 (1965). · Zbl 0129.43607 · doi:10.1063/1.1704288
[8] J. L. Lebowitz, J. K. Percus, and J. Sykes, ”Time evolution of the total distribution function of a one-dimensional system of hard rods,” Phys. Rev.,171, No. 1, 224-235 (1968). · doi:10.1103/PhysRev.171.224
[9] O. de Pazzis, ”Ergodic properties of a semiinfinite hard rods system,” Preprint (1971). · Zbl 0236.60071
[10] V. A. Rokhlin, ”Selected problems in the metric theory of dynamical systems,” Uspekh. Mat. Nauk,4, No. 2, 57-128 (1949).
[11] F. Spitzer, ”Uniform motion with elastic collision of an infinite particle system,” J. Math. Mech.,18, No. 10, 973-989 (1969). · Zbl 0184.21102
[12] T. E. Harris, ”Random measures and motions of point processes,” Z. Wahrscheindlichkeitstheorie,18, No. 2, 85-115 (1971). · Zbl 0194.49204 · doi:10.1007/BF00569182
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