scholarly journals Cube Root Fluctuations for the Corner Growth Model Associated to the Exclusion Process

2006 ◽  
Vol 11 (0) ◽  
pp. 1094-1132 ◽  
Author(s):  
Marton Balazs ◽  
Eric Cator ◽  
Timo Seppalainen
Keyword(s):  
Growth Model ◽  
Exclusion Process ◽  
Cube Root ◽  
Corner Growth Model

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model

2020 ◽  
Vol 8 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Coarse Graining ◽  
Exponential Weights ◽  
Percolation Process ◽  
Last Passage Percolation ◽  
Corner Growth Model ◽  
And Control

Abstract This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.

scholarly journals Non-existence of bi-infinite geodesics in the exponential corner growth model – Corrigendum

2021 ◽  
Vol 9 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Corner Growth Model

Random growth models

2018 ◽  
Author(s):  
Satya N. Majumdar
Keyword(s):  
Random Matrices ◽  
Growth Model ◽  
Growth Models ◽  
Exclusion Process ◽  
Fixed Time ◽  
Gaussian Unitary Ensemble ◽  
The Family ◽  
Asymmetric Simple Exclusion ◽  
Largest Eigenvalues ◽  
Unitary Ensemble

This article discusses the connection between a particular class of growth processes and random matrices. It first provides an overview of growth model, focusing on the TASEP (totally asymmetric simple exclusion process) with parallel updating, before explaining how random matrices appear. It then describes multi-matrix models and line ensembles, noting that for curved initial data the spatial statistics for large time t is identical to the family of largest eigenvalues in a Gaussian Unitary Ensemble (GUE multi-matrix model. It also considers the link between the line ensemble and Brownian motion, and whether this persists on Gaussian Orthogonal Ensemble (GOE) matrices by comparing the line ensembles at fixed position for the flat polynuclear growth model (PNG) and at fixed time for GOE Brownian motions. Finally, it examines (directed) last passage percolation and random tiling in relation to growth models.

scholarly journals Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Elnur Emrah ◽  
Christopher Janjigian ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Corner Growth Model

scholarly journals Stationary cocycles and Busemann functions for the corner growth model

2016 ◽  
Vol 169 (1-2) ◽  
pp. 177-222 ◽  
Author(s):  
Nicos Georgiou ◽  
Firas Rassoul-Agha ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Busemann Functions ◽  
Corner Growth Model

scholarly journals Geodesics and the competition interface for the corner growth model

2016 ◽  
Vol 169 (1-2) ◽  
pp. 223-255 ◽  
Author(s):  
Nicos Georgiou ◽  
Firas Rassoul-Agha ◽  
Timo Seppäläinen
Keyword(s):  
Growth Model ◽  
Corner Growth Model ◽  
Competition Interface
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