Painlevé Functions in Statistical Physics
نویسندگان
چکیده
We review recent progress in limit laws for the one-dimensional asymmetric simple exclusion process (ASEP) on the integer lattice. The limit laws are expressed in terms of a certain Painlevé II function. Furthermore, we take this opportunity to give a brief survey of the appearance of Painlevé functions in statistical physics. 2010 Mathematics Subject Classification: 34M55, 60K35, 82B23.
منابع مشابه
A numerical methodology for the Painlevé equations
The six Painlevé transcendents PI -PV I have both applications and analytic properties that make them stand out from most other classes of special functions. Although they have been the subject of extensive theoretical investigations for about a century, they still have a reputation for being numerically challenging. In particular, their extensive pole fields in the complex plane have often bee...
متن کاملThe relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation
We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlevé equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions which arise in the description of special function solutions of the fo...
متن کاملHypergeometric τ Functions of the q - Painlevé Systems of Type ( A 2 + A 1 ) ( 1 )
We consider a q-Painlevé III equation and a q-Painlevé II equation arising from a birational representation of the affine Weyl group of type (A2 + A1). We study their hypergeometric solutions on the level of τ functions.
متن کاملHypergeometric solutions to the q-Painlevé equations
It is well-known that the continuous Painlevé equations PJ (J=II,. . .,VI) admit particular solutions expressible in terms of various hypergeometric functions. The coalescence cascade of hypergeometric functions, from the Gauss hypergeometric function to the Airy function, corresponds to that of Painlevé equations, from PVI to PII [1]. The similar situation is expected for the discrete Painlevé...
متن کاملCONNECTION BETWEEN THE KdV EQUATION AND THE TWO - DIMENSIONAL ISING MODEL
Among the various profound but solvable models tion [41 of physics, two of the most studied are the Korteweg— d2v 1 dv 2 1 dv 1 de Vries (KdV) equation for nonlinear wave phenom—i + —(av~+ i3) + ‘yu3 +-~(2) enon [1] and the two-dimensional Ising model [2] for statistical mechanics. It has been known [3] for severwherey is the independent variable and a, j3, y, and 6 al years that a Painlevé tra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011