Ergodic theorems for coupled random walks and other systems with locally interacting components

Keywords

Ergodic theory, Mathematical proof, Mathematics, Computation, Invariant (physics)

References

• A characterization of the invariant measures for an infinite particle system with interactionsThomas M. Liggett — 1973
• Annihilating and coalescing random walks on ℤdDavid Griffeath — 1978
• Infinite Systems with Locally Interacting ComponentsFrank Spitzer — 1981
• Generalized potlatch and smoothing processesRichard A. Holley, Thomas M. Liggett — 1981
• Stochastic processes with Gaussian interaction of componentsCheng -Tan Hsiao — 1982
• An Infinite Particle System with Zero Range InteractionsThomas M. Liggett — 1973

Cited by

• Ergodic theorems and exponential decay of sample paths for certain interacting diffusion systemsTokuzo Shiga — 1992
• Neighbour-dependent point shifts and random exchange models: Invariance and attractorsAnton Muratov, Sergei Zuyev — 2013
• Large deviations and metastability in condensing stochastic particle systemsPaul Chleboun — 2011
• Extinction versus unbounded growth; Habilitation Thesis of the University Erlangen-NürnbergJan M. Swart — 2007
• Condensation in the Zero Range Process: Stationary and Dynamical PropertiesStefan Großkinsky, Gunter M. Schütz, Herbert Spohn — 2003
• A Note on the Central Limit Theorem for a Class of Linear SystemsYukio Nagahata, Nobuo Yoshida — 2009
• Branching random walks and multi-type contact-processes on the percolation cluster of Z^dDaniela Bertacchi, Fabio Zucca — 2013
• Coalescent processes arising in a study of diffusive clusteringAndreas Greven, Vlada Limic, Anita Winter — 2007
• On the role of Allee effect and mass migration in survival and extinction of a species.Davide Borrello — 2010
• On the long term behavior of some finite particle systemsJ. Theodore Cox, Andreas Greven — 1990
• Fixed points of the smoothing transformationRichard Durrett, Thomas M. Liggett — 1983
• Ecological equilibrium for restrained branching random walksDaniela Bertacchi, Gustavo Posta, Fabio Zucca — 2006
• Some ergodic theorems for a parabolic Anderson modelYong Liu, Yang Feng — 2012
• Branching-coalescing particle systemsSiva R. Arthreya, Jan M. Swart — 2005
• Time fluctuations of the random average process with parabolic initial conditionsLuiz Renato Fontes, Deborah Pereira de Medeiros, Marina Vachkovskaia — 2003
• Convergence in distribution of products of random matricesHarry Kesten, Frank Spitzer — 1984
• Reaction-diffusion processesMu-Fa Chen — 1998
• Continuous-Time Markov Decision Processes with Unbounded Transition and Discounted-Reward RatesHao Yan, Junyu Zhang, Xianping Guo — 2008
• Ergodicity of reversible reaction diffusion processesWanding Ding, Richard Durrett, Thomas M. Liggett — 1990
• A Note on the Diffusive Scaling Limit for a Class of Linear SystemsYukio Nagahata, Nobuo Yoshida — 2009

Related papers

• Ergodic Properties of the Random Walk Adic Transformation over the Beta TransformationMichael Bromberg — 2015
• On invariant measures for B-free systemsJoanna Kuaga-PrzymusMariusz Lema, Benjamin Weiss — 2014
• High Order Numerical Approximation of the Invariant Measure of Ergodic SDEsAssyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis — 2014
• On non-ergodic versions of limit theoremsDalibor Volný — 1989
• Absolutely continuous, invariant measures for dissipative, ergodic transformationsJon Aaronson, Tom Meyerovitch — 2005
• Certain properties of smooth cocycles over flows with an invariant ergodic measureВ. А. Плисс — 1987