Stationary coalescing walks on the lattice

DOI10.1007/s00440-018-0893-2zbMath1434.37004arXiv1612.00434OpenAlexW2904373552WikidataQ128724758 ScholiaQ128724758MaRDI QIDQ2334363

Arjun Krishnan, Jon Chaika

Publication date: 7 November 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.00434

zbMATH Keywords

geodesicsfirst-passage percolationmeasure-preserving transformationsbi-infinite trajectories

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Processes in random environments (60K37)

Related Items

Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation, Random nearest neighbor graphs: the translation invariant case, Weakly mixing smooth planar vector field without asymptotic directions, Existence, uniqueness and coalescence of directed planar geodesics: proof via the increment-stationary growth process, Stationary coalescing walks on the lattice II: entropy, Absence of backward infinite paths for first-passage percolation in arbitrary dimension, Strongly mixing smooth planar vector field without asymptotic directions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational formulas and cocycle solutions for directed polymer and percolation models
• First passage percolation on a hyperbolic graph admits bi-infinite geodesics
• Geodesics and the competition interface for the corner growth model
• Density and uniqueness in percolation
• Coexistence for Richardson type competing spatial growth models
• Coexistence in two-type first-passage percolation models
• Infinite clusters in percolation models
• Geodesics in two-dimensional first-passage percolation
• Busemann functions and infinite geodesics in two-dimensional first-passage percolation
• Variational Formula for the Time Constant of First-Passage Percolation
• Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting
• Weakly Mixing Transformations Which are Not Strongly Mixing