scholarly journals The oriented swap process and last passage percolation

2021 ◽  
Author(s):  
Elia Bisi ◽  
Fabio Deelan Cunden ◽  
Shane Gibbons ◽  
Dan Romik
Keyword(s):  
Last Passage Percolation

scholarly journals Local stationarity in exponential last-passage percolation

2021 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Brownian Motion ◽  
Total Variation ◽  
High Probability ◽  
Probabilistic Methods ◽  
Side Length ◽  
Last Passage Percolation ◽  
Last Passage Times ◽  
Starting Point ◽  
Point To Point ◽  
Passage Times

AbstractWe consider point-to-point last-passage times to every vertex in a neighbourhood of size $$\delta N^{\nicefrac {2}{3}}$$ δ N 2 3 at distance N from the starting point. The increments of the last-passage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on $$\delta $$ δ . Through this result we show that (1) the $$\text {Airy}_2$$ Airy 2 process is locally close to a Brownian motion in total variation; (2) the tree of point-to-point geodesics from every vertex in a box of side length $$\delta N^{\nicefrac {2}{3}}$$ δ N 2 3 going to a point at distance N agrees inside the box with the tree of semi-infinite geodesics going in the same direction; (3) two point-to-point geodesics started at distance $$N^{\nicefrac {2}{3}}$$ N 2 3 from each other, to a point at distance N, will not coalesce close to either endpoint on the scale N. Our main results rely on probabilistic methods only.

Lower deviations in β-ensembles and law of iterated logarithm in last passage percolation

2021 ◽  
Author(s):  
Riddhipratim Basu ◽  
Shirshendu Ganguly ◽  
Milind Hegde ◽  
Manjunath Krishnapur
Keyword(s):  
Law Of Iterated Logarithm ◽  
Last Passage Percolation ◽  
Iterated Logarithm

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 On the local fluctuations of last-passage percolation models

2015 ◽  
Vol 125 (2) ◽  
pp. 538-551 ◽  
Author(s):  
Eric Cator ◽  
Leandro P.R. Pimentel
Keyword(s):  
Last Passage Percolation ◽  
Local Fluctuations

scholarly journals Pfaffian Schur processes and last passage percolation in a half-quadrant

2018 ◽  
Vol 46 (6) ◽  
pp. 3015-3089 ◽  
Author(s):  
Jinho Baik ◽  
Guillaume Barraquand ◽  
Ivan Corwin ◽  
Toufic Suidan
Keyword(s):  
Last Passage Percolation

scholarly journals Coalescence of geodesics in exactly solvable models of last passage percolation

2019 ◽  
Vol 60 (9) ◽  
pp. 093301
Author(s):  
Riddhipratim Basu ◽  
Sourav Sarkar ◽  
Allan Sly
Keyword(s):  
Exactly Solvable Models ◽  
Solvable Models ◽  
Last Passage Percolation ◽  
Exactly Solvable

scholarly journals Exponents governing the rarity of disjoint polymers in Brownian last passage percolation

2020 ◽  
Vol 120 (3) ◽  
pp. 370-433
Author(s):  
Alan Hammond
Keyword(s):  
Last Passage Percolation
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