There are two main directions of my interests: 1) the large deviations in queuing systems, 2) Gibbs random fields. In the collaborations with R. Dobrushin a large deviation principle was proved for processes with independent increments. The result has a form applicable to queuing systems. Tandem queuing systems were studied by this result. The bottle neck effect was proved under a large delay in the tandem system. The large deviations of different systems were studied as well. In the collaborations with R. Dobrushin a criterium of the Gibbs state uniqueness for non-compact spin spaces was obtained. The result was applied to studies of the uniqueness region of a non-ideal gas state. Some works are devoted to applications of the Gibbs field theory to the image processing.
Biography
In 1967 graduated from Novosibirsk State University. In 1975 Ph.D. thesis was defended.
Main publications:
E. Pechersky. The Peierls Condition (or GPS Condition) Is Not Always Satisfied // Sel. Math. Sov., 3, 1, 1983/84, 87–91.
F. I. Karpelevich, E. A. Pechersky, Yu. M. Suhov. A Phase Transition for Hyperbolic branching processes // Commun. Math. Phys., 195, 627–642, 1998.
F. Tupin, H. Maitre, J. F. Mangin, J. M. Nicolas, E. Pechersky. Detection of Linear Feature in SAR Images: Application to Road Network Extraction // IEEE Transactions on Geoscience and Remote Sensing, 36, 2, 1998, 434–453.
E. Pechersky, Yu. Zhukov. Uniqueness of Gibbs State for Non-Ideal Gas in ${\bf R}^d$: the case of pair potentials // J. Stat. Phys. 97, 1/2, 1999, 145–172.
E. Pechersky, S. Pirogov, G. M. Schütz, A. Vladimirov, A. Yambartsev, “Large emission regime in mean field luminescence”, Mosc. Math. J., 19:1 (2019), 107–120
E. A. Pechersky, S. A. Pirogov, G. M. Schütz, A. A. Vladimirov, A. A. Yambartsev, “Large fluctuations in two-level systems with stimulated emission”, TMF, 198:1 (2019), 133–144; Theoret. and Math. Phys., 198:1 (2019), 118–128
Eugene Pechersky, Elena Petrova, Sergey Pirogov, “Phase transitions of laminated models at any temperature”, Mosc. Math. J., 10:4 (2010), 789–806
2008
4.
N. D. Vvedenskaya, E. A. Pechersky, “Circle of Interacting Servers: Spontaneous Collective Behavior in the Case of Large Fluctuations”, Probl. Peredachi Inf., 44:4 (2008), 92–108; Problems Inform. Transmission, 44:4 (2008), 370–384
N. D. Vvedenskaya, E. A. Pechersky, Yu. M. Sukhov, “Large Deviations in Some Queueing Systems”, Probl. Peredachi Inf., 36:1 (2000), 48–59; Problems Inform. Transmission, 36:1 (2000), 42–53
R. L. Dobrushin, E. A. Pechersky, “Large Deviations for Random Processes with Independent Increments on Infinite Intervals”, Probl. Peredachi Inf., 34:4 (1998), 76–108; Problems Inform. Transmission, 34:4 (1998), 354–382
E. A. Pechersky, S. B. Shlosman, “Low-temperature phase transitions in systems with one ground state”, TMF, 70:3 (1987), 462–468; Theoret. and Math. Phys., 70:3 (1987), 325–330
A. A. Mogul'skii, E. A. Pechersky, “On the time of the first hit in a domain with a curved boundary”, Sibirsk. Mat. Zh., 19:4 (1978), 824–841; Siberian Math. J., 19:4 (1978), 582–595
A. A. Mogul'skiĭ, E. A. Pečerskiĭ, “On the first exit time out of a semigroup in $R^m$ for a random walk”, Teor. Veroyatnost. i Primenen., 22:4 (1977), 837–844; Theory Probab. Appl., 22:4 (1978), 818–825
E. A. Pechersky, “Remarks on the weak bicompactness of a net of positive measures”, Sibirsk. Mat. Zh., 16:6 (1975), 1240–1245; Siberian Math. J., 16:6 (1975), 951–955
11.
A. A. Borovkov, E. A. Pechersky, “Convergence of the distributions of integral functionals”, Sibirsk. Mat. Zh., 16:5 (1975), 899–915; Siberian Math. J., 16:5 (1975), 685–698
E. A. Pechersky, “Some identities related to the exit of a random walk out of a segment and a semi-interval”, Teor. Veroyatnost. i Primenen., 19:1 (1974), 104–119; Theory Probab. Appl., 19:1 (1974), 106–121
A. A. Borovkov, E. A. Pechersky, “Criteria for weak convergence of nonnegative measures, and $\sigma$-topological spaces”, Dokl. Akad. Nauk SSSR, 208:1 (1973), 18–20
1970
14.
E. A. Pechersky, “A criterion for the extendability of measures with values in a group”, Sibirsk. Mat. Zh., 11:6 (1970), 1409–1415; Siberian Math. J., 11:6 (1970), 1035–1039
1969
15.
E. A. Pechersky, “Extension of measures with values in a group”, Sibirsk. Mat. Zh., 10:3 (1969), 710–711; Siberian Math. J., 10:3 (1969), 515–516
16.
E. A. Pechersky, B. A. Rogozin, “Transformations of joint distributions of random variables connected with fluctuations of a process with independent increments”, Teor. Veroyatnost. i Primenen., 14:3 (1969), 431–444; Theory Probab. Appl., 14:3 (1969), 410–423
E. A. Zhizhina, V. A. Zagrebnov, Yu. M. Kondrat'ev, V. A. Malyshev, B. S. Nakhapetian, E. A. Pechersky, S. A. Pirogov, S. K. Pogosyan, Ya. G. Sinai, “Robert Adol'fovich Minlos (28 February 1931 – 9 January 2018)”, TMF, 195:1 (2018), 3–5; Theoret. and Math. Phys., 195:1 (2018), 491–493
2001
18.
N. D. Vvedenskaya, E. B. Dynkin, A. Ya. Kreinin, N. A. Kuznetsov, V. A. Malyshev, R. A. Minlos, I. A. Ovseevich, E. A. Pechersky, A. N. Rybko, Yu. M. Sukhov, “Fridrikh Izrailevich Karpelevich. In Memoriam”, Probl. Peredachi Inf., 37:2 (2001), 110–111; Problems Inform. Transmission, 37:2 (2001), 185–186
1997
19.
E. A. Pechersky, Yu. M. Sukhov, “Dobrushin's ideas in the theory of queuing networks”, Uspekhi Mat. Nauk, 52:2(314) (1997), 25–30; Russian Math. Surveys, 52:2 (1997), 265–269
L. A. Bassalygo, V. A. Malyshev, R. A. Minlos, I. A. Ovseevich, E. A. Pechersky, M. S. Pinsker, V. V. Prelov, A. N. Rybko, Yu. M. Sukhov, S. B. Shlosman, “In Memory of Roland L'vovich Dobrushin”, Probl. Peredachi Inf., 32:3 (1996), 3–24; Problems Inform. Transmission, 32:3 (1996), 223–238
Мини-конференция в память Р.А. Минлоса: V. M. Tikhomirov, A. M. Vershik, V. A. Malyshev, M. L. Blank, G. A. Kabatiansky, S. Shlosman, B. M. Gurevich, E. A. Zhizhina, E. A. Pechersky, A. G. Tarasov, S. A. Stepin Dobrushin Mathematics Laboratory Seminar February 27, 2018 15:00
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