A PDE for the joint distributions of the Airy Process
نویسندگان
چکیده
In this paper, we answer a question posed by Kurt Johansson, to find a PDE for the joint distribution of the Airy Process. The latter is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion, when the number of particles get large, with space and time appropriately rescaled. The question reduces to an asymptotic analysis on the equation, governing the joint probability of the eigenvalues of coupled Gaussian Hermitian matrices.
منابع مشابه
0 Se p 20 04 PDE ’ s for the joint distributions of the Dyson , Airy and Sine processes
In a celebrated paper, Dyson shows that the spectrum of a n× n randomHermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n non-colliding Brownian motions held together by a drift term. The universal edge and bulk scalings for Hermitian random matrices, applied to the Dyson process, lead to the Airy and Sine processes. In particular, the Airy process is a continuou...
متن کاملM ar 2 00 4 PDE ’ s for the joint distributions of the Dyson , Airy and Sine processes
In a celebrated paper, Dyson shows that the spectrum of a n× n randomHermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n non-colliding Brownian motions held together by a drift term. The universal edge and bulk scalings for Hermitian random matrices, applied to the Dyson process, lead to the Airy and Sine processes. In particular, the Airy process is a continuou...
متن کاملA PDE for the Multi-Time Joint Probability of the Airy Process
This paper gives a PDE for multi-time joint probability of the Airy process, which generalizes Adler and van Moerbeke’s result on the 2-time case. As an intermediate step, the PDE for the multi-time joint probability of the Dyson Brownian motion is also given.
متن کامل1 9 A pr 2 00 4 PDE ’ s for the joint distributions of the Dyson , Airy and Sine processes
In a celebrated paper, Dyson shows that the spectrum of a n× n randomHermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n non-colliding Brownian motions held together by a drift term. The universal edge and bulk scalings for Hermitian random matrices, applied to the Dyson process, lead to the Airy and Sine processes. In particular, the Airy process is a continuou...
متن کاملElzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions
In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified t...
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 2003