On the local fluctuations of last-passage percolation models

被引：18

作者：

Cator, Eric ^{[1
]}

Pimentel, Leandro P. R. ^{[2
]}

机构：

[1] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, NL-6525 AJ Nijmegen, Netherlands

[2] Univ Fed Rio de Janeiro, Inst Math, BR-21941909 Rio De Janeiro, RJ, Brazil

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 02期

关键词：

GROWTH;

D O I：

10.1016/j.spa.2014.08.009

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Using the fact that the Airy process describes the limiting fluctuations of the Hammersley last-passage percolation model, we prove that it behaves locally like a Brownian motion. Our method is quite straightforward, and it is based on a certain monotonicity and good control over the equilibrium measures of the Hammersley model (local comparison). (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：538 / 551

页数：14

共 50 条

[31] Last-passage algorithms for corner charge singularity of conductors
Hwang, CO
Won, T
JOURNAL OF THE KOREAN PHYSICAL SOCIETY, 2005, 47 : S464 - S466
[32] Busemann functions and equilibrium measures in last passage percolation models
Cator, Eric
Pimentel, Leandro P. R.
PROBABILITY THEORY AND RELATED FIELDS, 2012, 154 (1-2) : 89 - 125
[33] Busemann functions and equilibrium measures in last passage percolation models
Eric Cator
Leandro P. R. Pimentel
Probability Theory and Related Fields, 2012, 154 : 89 - 125
[34] Coalescence of geodesics in exactly solvable models of last passage percolation
Basu, Riddhipratim
Sarkar, Sourav
Sly, Allan
JOURNAL OF MATHEMATICAL PHYSICS, 2019, 60 (09)
[35] Optimality Regions and Fluctuations for Bernoulli Last Passage Models
Nicos Georgiou
Janosch Ortmann
Mathematical Physics, Analysis and Geometry, 2018, 21
[36] Optimality Regions and Fluctuations for Bernoulli Last Passage Models
Georgiou, Nicos
Ortmann, Janosch
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2018, 21 (03)
[37] Modulus of continuity for polymer fluctuations and weight profiles in Poissonian last passage percolation
Hammond, Alan
Sarkar, Sourav
ELECTRONIC JOURNAL OF PROBABILITY, 2020, 25
[38] Last-Passage Algorithm for Charge Distribution Over a Finite Region
Jang, Hoseung
Given, James
Yu, Unjong
Hwang, Chi-Ok
ADVANCED THEORY AND SIMULATIONS, 2021, 4 (02)
[39] Fluctuations in first-passage percolation
Sosoe, Philippe
RANDOM GROWTH MODELS, 2018, 75 : 69 - 93
[40] On the Passage Time Geometry of the Last Passage Percolation Problem
Alberts, Tom
Cator, Eric
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2021, 18 (01): : 211 - 247

← 1 2 3 4 5 →