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Selecta II: Probability Theory, Statistical Mechanics, Mathematical Physics and Mathematical Fluid Dynamics 2010 ed. [Pehme köide]

  • Formaat: Paperback / softback, 514 pages, kõrgus x laius: 235x155 mm, kaal: 813 g, 53 Illustrations, color; 11 Illustrations, black and white; XX, 514 p. 64 illus., 53 illus. in color. With New printing in a different form., 1 Paperback / softback
  • Sari: Springer Collected Works in Mathematics
  • Ilmumisaeg: 11-Nov-2019
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1493997882
  • ISBN-13: 9781493997886
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Selecta II: Probability Theory, Statistical Mechanics, Mathematical Physics and Mathematical Fluid Dynamics 2010 ed.Suurem pilt
  • Formaat: Paperback / softback, 514 pages, kõrgus x laius: 235x155 mm, kaal: 813 g, 53 Illustrations, color; 11 Illustrations, black and white; XX, 514 p. 64 illus., 53 illus. in color. With New printing in a different form., 1 Paperback / softback
  • Sari: Springer Collected Works in Mathematics
  • Ilmumisaeg: 11-Nov-2019
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1493997882
  • ISBN-13: 9781493997886
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781493997886.html

This book collects 20 papers that span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields.



The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997).  He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.This volume follows Volume I.

From the reviews:

"The second volume covers statistical mechanics and related topics. It contains 22 papers divided into four groups: Part I: Probability Theory; Part II: Statistical Mechanics; Part III: Mathematical Physics; Part IV: Mathematical Fluid Dynamics. The volume represents Sinai’s work on the above topics spanning almost 40 years: the earliest paper is dated 1972, and the latest 2008. The choice of papers was made by Sinai himself, and he provides commentary for each one. The reader will ?nd a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinai’s personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results." (Nikolai Chernov, Mathematical Reviews 2012e)


Arvustused

From the reviews:

The second volume covers statistical mechanics and related topics. It contains 22 papers divided into four groups . The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinais personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results. (Nikolai Chernov, Mathematical Reviews, Issue 2012 e)

VOLUME 2
Probability Theory, Statistical Mechanics, Mathematics Physics and Mathematical Fluid Dynamics
Part I Probability Theory
1 Simple Random Walks on Tori. J. Statist. Phys., 94 (1999). no. 3/4.695-708
3(15)
2 The limiting behavior of a one-dimensional random walk in a random medium, Teor. Veroyatnost. i Primenen., 27 (1982), no. 2, 247-258; translated in Theory Probab., 27 (1982). no. 2, 256-268
18(14)
3 A remark concerning random walks with random potentials. Fund. Math., 147 (1995), no. 2, 173-180
32(9)
4 A Random Walk with Random Potential. Teor. Veroyatnost. i Primenen., 38 (1993), no. 2.457-460: translated in Theory Probab. Appl., 38 (1993), no.
2. 382-385
41(5)
5 Distribution of some junctionals of the integral of a random walk. Teoret. Mat. Fiz., 90 (1992). no. 3, 323-353. translated in Theoret. Math. Phys 90 (1992), no.
3. 219-241
46(27)
II Statistical Mechanics
1 Construction of dynamics in one-dimensional systems of statistical mechanics, Teoret. Mat. Fiz., 11 (1972), no.
2. 248-258, translated in Theoret. Math. Phys., 11 (1972), no. 2, 487-494
73(9)
2 (With S. A. Pirogov). Phase diagrams of classical lattice systems, Teoret. Mat. Fiz., 25 (1975), no. 3, 358-369: translated in Theoret. Math. Phys 25 (1975). no.
3. 1185-1192. (with S. A. Pirogov), Phase diagrams of classical lattice systems (continuation), Teoret. Mat. Fiz., 26 (1976), no. 1, 61-76; translated in Theoret. Math. Phys 26 (1976). no. 1, 39-49
82(20)
3 (With E. I. Dinaburg). An analysis of ANNNI model by Peierl's contour method. Comm. Math. Phys 98 (1985). no.
1. 119-144
102(27)
4 (With P. M. Bleher). Critical indices for Dyson's asymptotically-hierarchical models. Comm. Math. Phys 45 (1975), no. 3, 247-278
129(33)
5 (With P. M. Bleher) Investigation of the critical point in models of the type of Dyson's hierarchical models. Comm. Math. Phys, 33 (1973), no. I. 23-42
162(29)
III Mathematical Physics
1 (With E. I, Dinaburg), The one-dimensional Schrodinger equation with a quasiperiodic potential, Funkcional. Ana), i Prilozen., 9 (1975), no. 4, 8-21; translated in Funct. Anal. Appl, 9 (1975), no. 4, 279-289
191(12)
2 (With P. Bleher and D. Kosygin), Distribution of Energy Levels of Quantum Free Particle on the Liouville Surface and Trace Formulae, Comm. Math. Phys., 170 (1995), no. 2, 375-403
203(30)
3 Mathematical problems in the theory of quantum chaos. Geometric aspects of functional analysis (1989-90), 41-59, Lecture Notes in Math., 1469, Springer, Berlin, 1991
233(20)
4 Dynamics of a heavy particle surrounded by a finite number of light particles, Teoret. Mat. Fiz 121 (1999), No. 1, 110-116; translated as Theoret. and Math. Phys 121 (1999). no. 1, 1351-1357
253(8)
5 (With A. I. Neishtadt), Adiabatic piston as a dynamical system, J. Statist. Phys. 116 (2004), no. 1-4, 815-820
261(7)
6 Poisson distribution in a geometric problem. Dynamical systems and statistical mechanics (Moscow, 1991), 199-214, Adv. Soviet Math., 3, Amer. Math. Soc., Providence. RI, 1991
268(21)
IV Mathematical Fluid Dynamics
1 (With Weinan E, K. Khanin, and A. Mazel), Invariant Measures for Burgers Equation with Stochastic Forcing, Ann. of Math. (2). 151 (2000), no. 3, 877-960
289(86)
2 (With J. Mattingly), An Elementary Proof of the Existence and Uniqueness Theorem for Navier-Stokes Equations, Commun. in Contemp. Math., 1 (1999), no. 4, 497-516
375(21)
3 Statistics of shocks in solutions of Inviscid Burgers equation, Comm. Math. Phys., 148 (1992), no. 3, 601-621
396(22)
4 (With Weinan E and J. Mattingly), Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Comm. Math. Phys 224 (2001). no. 1, 83-106
418(25)
5 (With D. Li), Blow ups of complex solutions of the 3D-Navier-Stokes system and renormalization group method. J. Eur. Math. Soc. (JEMS), 10 (2008), no. 2,267-313
443(58)
6 Two results concerning asymptotic behavior of solutions of the Burgers equation with force, J. Statist. Phys., 64 (1991), no. 1-2, 1-12
501