QUANTUM ERGODICITY ON LARGE REGULAR GRAPHS

被引：50

作者：

Anantharaman, Nalini ^{[1
]}

Le Masson, Etienne ^{[1
]}

机构：

[1] Univ Paris 11, Math, Orsay, France

来源：

DUKE MATHEMATICAL JOURNAL | 2015年 / 164卷 / 04期

基金：

美国国家科学基金会;

关键词：

SEMICIRCLE LAW; DELOCALIZATION; EIGENFUNCTIONS; EIGENVALUES; CHAOS;

D O I：

10.1215/00127094-2881592

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose a version of the quantum ergodicity theorem on large regular graphs of fixed valency. This is a property of delocalization of "most" eigenfunctions. We consider expander graphs with few short cycles (for instance random large regular graphs). Our method mimics the proof of quantum ergodicity on manifolds: it uses microlocal analysis on regular trees, as introduced by the second author in an earlier paper.

引用

页码：723 / 765

页数：43

共 40 条

[1] EIGENVALUES AND EXPANDERS [J].