[图书][B] 50 years of first-passage percolation
A Auffinger, M Damron, J Hanson - 2017 - books.google.com
First-passage percolation (FPP) is a fundamental model in probability theory that has a wide
range of applications to other scientific areas (growth and infection in biology, optimization in …
range of applications to other scientific areas (growth and infection in biology, optimization in …
The stationary horizon and semi-infinite geodesics in the directed landscape
The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …
Nonexistence of bigeodesics in planar exponential last passage percolation
Bi-infinite geodesics are fundamental objects of interest in planar first passage percolation.
A longstanding conjecture states that under mild conditions there are almost surely no …
A longstanding conjecture states that under mild conditions there are almost surely no …
Coalescence of geodesics in exactly solvable models of last passage percolation
Coalescence of semi-infinite geodesics remains a central question in planar first passage
percolation. In this paper, we study finer properties of the coalescence structure of finite and …
percolation. In this paper, we study finer properties of the coalescence structure of finite and …
Infinite geodesics, competition interfaces and the second class particle in the scaling limit
We establish fundamental properties of infinite geodesics and competition interfaces in the
directed landscape. We construct infinite geodesics in the directed landscape, establish their …
directed landscape. We construct infinite geodesics in the directed landscape, establish their …
Cube root fluctuations for the corner growth model associated to the exclusion process
We study the last-passage growth model on the planar integer lattice with exponential
weights. With boundary conditions that represent the equilibrium exclusion process as seen …
weights. With boundary conditions that represent the equilibrium exclusion process as seen …
Exponents governing the rarity of disjoint polymers in Brownian last passage percolation
A Hammond - Proceedings of the London Mathematical …, 2020 - Wiley Online Library
In last passage percolation models lying in the KPZ universality class, long maximizing
paths have a typical deviation from the linear interpolation of their endpoints governed by …
paths have a typical deviation from the linear interpolation of their endpoints governed by …
Fractal geometry of the space-time difference profile in the directed landscape via construction of geodesic local times
S Ganguly, L Zhang - arXiv preprint arXiv:2204.01674, 2022 - arxiv.org
The Directed Landscape, a random directed metric on the plane (where the first and the
second coordinates are termed spatial and temporal respectively), was constructed in the …
second coordinates are termed spatial and temporal respectively), was constructed in the …
Thermodynamic limit for directed polymers and stationary solutions of the Burgers equation
Y Bakhtin, L Li - Communications on Pure and Applied …, 2019 - Wiley Online Library
The first goal of this paper is to prove multiple asymptotic results for a time‐discrete and
space‐continuous polymer model of a random walk in a random potential. These results …
space‐continuous polymer model of a random walk in a random potential. These results …
Stationary cocycles and Busemann functions for the corner growth model
N Georgiou, F Rassoul-Agha… - Probability Theory and …, 2017 - Springer
We study the directed last-passage percolation model on the planar square lattice with
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …
nearest-neighbor steps and general iid weights on the vertices, outside of the class of …