Statistical Ergodic Theorem in Symmetric Spaces for Infinite Measures

Ergodic theorem, ergodic theory, and statistical mechanics.

This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

0 Infinite Random Matrices and Ergodic Measures

We introduce and study a 2–parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a determinantal point process on the real line. The correlation kernel for this process is explicitly computed. At certain values of parameters the kernel turns into...

A Weak Ergodic Theorem for Infinite Products of Lipschitzian Mappings

Let K be a bounded, closed, and convex subset of a Banach space. For a Lipschitzian self-mapping A of K , we denote by Lip(A) its Lipschitz constant. In this paper, we establish a convergence property of infinite products of Lipschitzian self-mappings of K . We consider the set of all sequences {At}t=1 of such selfmappings with the property limsupt→∞ Lip(At) ≤ 1. Endowing it with an appropriate...

a mean ergodic theorem for asymptotically quasi-nonexpansive affine mappings in banach spaces satisfying opial's condition