Historical Lattice Trees

被引：1

作者：

Cabezas, Manuel ^{[1
]}

Fribergh, Alexander ^{[2
]}

Holmes, Mark ^{[3
]}

Perkins, Edwin ^{[4
]}

机构：

[1] Pontificia Univ Catolica Chile, Santiago, Chile

[2] Univ Montreal, Montreal, PQ, Canada

[3] Univ Melbourne, Sch Math & Stat, Melbourne, Vic, Australia

[4] Univ British Columbia, Math Dept, Vancouver, BC, Canada

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2023年 / 401卷 / 01期

基金：

加拿大自然科学与工程研究理事会; 澳大利亚研究理事会;

关键词：

SUPER-BROWNIAN MOTION; INDUCTIVE APPROACH; CONVERGENCE;

D O I：

10.1007/s00220-023-04641-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove that the rescaled historical processes associated to critical spread-out lattice trees in dimensions d > 8 converge to historical Brownian motion. This is a functional limit theorem for measure-valued processes that encodes the genealogical structure of the underlying random trees. Our results are applied elsewhere to prove that random walks on lattice trees, appropriately rescaled, converge to Brownian motion on super-Brownian motion.

引用

页码：435 / 496

页数：62

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