International Journal of Probability and Statistics

International Journal of Probability and Statistics aims to publish refereed, well-written original research articles, and studies that describe the latest research and developments in the area of probability and statistics, and to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in the area of Probability and Statistics.

## Michael Blank

Editorial Board Member of International Journal of Probability and Statistics

Professor, Russian Academy of Sciences, Inst. For Information Transmission Problems, Russia

Research Areas

Ergodic Theory, Dynamical Systems, Probability Theory

### Education

 1998 Doctor Russian Academy of Sciences 1985 Ph.D Moscow State University

### Experience

 1994-present Russian Academy of Sciences, Inst. forInformation Transmission Problems, Principal Scientific Researcher 2000-present Moscow Independent University, Professor 1992-present Laboratoire Cassiopee UMR6202, CNRS, France, (Spring term), Visiting Professor 2001-2002 School of Mathematics, Georgia Institute of Technology (Fall term), Visiting Professor 1986-1993 Russian Academy of Sciences, Inst. General Genetics, Senior Scientific Researcher 1983-1985 Math. Dept. Moscow State Univ., Ph.D. student 1975-1986 Laboratory of mathematical methods, All Union Centre of Cardiology, Sci. Researcher

### Membership

 1986-present, member of Moscow Mathematical Society 1991-present, member of American Mathematical Society 1991-present, member of International Soc. of Math. Phys

### Publications: Conferences/Workshops/Symposiums/Journals/Books

 [1] Metric properties of $\epsilon$-trajectories of dynamicalsystems with stochastic behaviour, Erg. Th. and Dyn.Systems, 8:3 (1988), 365-378. [2] Metric properties of minimal solutions of discrete periodical variational problems, Nonlinearity, 2 (1989), 1-22. [3] Small perturbations of chaotic dynamical systems, Uspekhi Matem. Nauk, 44:6 (1989), 3-28. [4] Chaos and order in multidimensional Frenkel-Kontorova model, Theor. and Math. Phys., 85:3 (1990), 349-367. [5] Marginal singularities, almost invariant sets, and small perturbations, Chaos, 1:3 (1991), 347-356. [6] (with Altukhov Yu.P.) Genetic dynamics of population systems with varying parameters of structure and selection, Dokl. Ac. Sci. (Russia), 326:6 (1992), 1068-1072. [7] Singular phenomena in chaotic dynamical systems, Dokl. Ac. Sci. (Russia), 328:1 (1993), 7-11. [8] (with Biferale L., Frisch U.) Chaotic cascades with Kolmogorov 1941 scaling, J.Stat. Phys. 75:5-6 (1994), 781-795. (mp_arc/94-53) [9] Pathologies generated by round-off in dynamical systems, Physica D, 78:1-2 (1994), 93-114. (mp_arc/94-54) [10] Geometric constructions in multifractality formalism, In: Levy Flights and Applications in Physics, eds M.Shlesinger, G.M.Zaslavsky, U.Frisch, Lect. Notes in Phys. (Springer, Berlin), v.450 (1995), 140-150. [11] Round-off induced instabilities and some unusual arithmetics, Comptes Rendus CRAS, II, 321 (1995), 139-145. [12] (with Altukhov Yu.P.) Nonequilibrium genetic dynamics of population systems, Dokl. Ac. Sci. (Russia), 344:1(1995), 136-139. [13] Multiplicative cascade models and multifractality, in: Small-Scale Structures in Three-Dimensional Hydro and Magnetohydronamic Turbulence, eds M.Meneguzzi, A.Pouquet, P.L.Sulem. Lect. Notes Phys., 462(1995), 159-165, Spr.-Verlag. [14] (with Keller G.) Stochastic stability versus localization in one-dimensional dynamical systems, Nonlinearity, 10:1(1997), 81-107. (chao-dyn/9602011) [15] Discreteness and continuity in problems of chaotic dynamics, Monograph, Amer. Math. Soc., 1997. [16] Generalized phase transitions in finite coupled map lattices, Physica D, 103(1997), 34-50. (chao-dyn/9511005) [17] (with Jogi P. and Sornette D.), Fine structure and complex exponents in power-law distributions from random maps, Phys. Rev. E 57:1(1998), 120-134. [18] (with Keller G.) Random perturbations of chaotic dynamical systems: stability of the spectrum, Nonlinearity, 11(1998), 1351-1364. (chao-dyn/9712016) [19] Mozer theorem about an invariant curve and round-off errors, Uspekhi Mat. Nauk, 53:4 (1998), 188-189. (chao-dyn/9706005) [20] (with Altukhov Yu.P.) Genetic dynamics of population systems represented by small subpopulations: analytic modeling and numerical results, Genetics, 35:11 (1999), 1572-1584. [21] Variational principles in the analysis of traffic flows, (Why it is worth to go against the flow.), Markov Processes and Related Fields, 6:3(2000), 287-304. (mp_arc/00-122) [22] Dynamics of traffic jams: order and chaos, Moscow Math. J., 1:1 (2001), 1-26. (mp_arc/01-40) [23] Stability and localization in chaotic dynamics, Monograph, MCCME, Moscow, 2001. [24] Perron-Frobenius spectrum for random maps and its approximation, Moscow Math. J., 1:3 (2001), 315-344. (mp_arc/01-218) [25] (with Keller G. and Liverani C.), Ruelle-Perron-Frobenius spectrum for Anosov maps, Nonlinearity, 15:6(2002), 1905-1973. (mp_arc/01-140) [26] (with Bunimovich L.) Multicomponent dynamical systems: SRB measures and phase transitions, Nonlinearity, 16:1(2003), 387-401. (math.DS/0202200) [27] Ergodic properties of a simple deterministic traffic flow model, J. Stat. Phys., 111:3-4(2003), 903-930. (math.DS/0206194) [28] (with Bunimovich L.) Switched flow systems: pseudo billiard dynamics, Dynamical Systems, 19:4(2004), 359-370. (math.DS/0408241) [29] Hysteresis phenomenon in deterministic traffic flows, J. Stat. Phys. 120: 3-4(2005), 627-658. (math.DS/0408240) [30] (with Bunimovich L.) Long range action in networks of chaotic elements, Nonlinearity, 19:2 (2006) 329-344. (math.DS/0505610) [31] On raw coding of chaotic dynamics, Probl. Information Transmission, 42:1(2006), 72-77. (math.DS/0603575) [32] (with Pirogov S.) On quasi-successful couplings of Markov processes, Probl. Information Transmission, 43:4(2007), 51-67. (math.PR/0610118) [33] Finite rank approximations of expanding maps with neutral singularities, Discrete and Continuous Dyn. Systems, Ser A, 21:3(2008), 749-762. arXiv:0709.2564 math.DS) [34] Travelling with/against the Flow. Deterministic Diffusive Driven Systems, J. Stat. Phys., 133:4(2008), 773-796. (arXiv:0810.2205 math.DS) [35] Collective phenomena in lattices of weakly interacting maps, Doklady Akademii Nauk (Russia), 430:3(2010), 300-304. [36] Metric properties of discrete time exclusion type processes in continuum, J. Stat. Phys., 140:1(2010), 170-197. (arXiv:0904.4585 math.DS) [37] Self-Consistent Mappings and Systems of Interacting Particles, Doklady Akademii Nauk (Russia), 436:3(2011), 295-298. [38] Exclusion type spatially heterogeneous processes in continuum, J. Stat. Mech. (2011) P06016