Local problems on trees from the perspectives of distributed algorithms, finitary factors, and descriptive combinatorics
We study connections between distributed local algorithms, finitary factors of iid processes,
and descriptive combinatorics in the context of regular trees. We extend the Borel …
and descriptive combinatorics in the context of regular trees. We extend the Borel …
Factors of IID on trees
Classical ergodic theory for integer-group actions uses entropy as a complete invariant for
isomorphism of IID (independent, identically distributed) processes (aka product measures) …
isomorphism of IID (independent, identically distributed) processes (aka product measures) …
Poisson splitting by factors
Given a homogeneous Poisson process on ℝ d with intensity λ, we prove that it is possible to
partition the points into two sets, as a deterministic function of the process, and in an …
partition the points into two sets, as a deterministic function of the process, and in an …
Point processes, cost, and the growth of rank in locally compact groups
Let G be a locally compact, second countable, unimodular group that is nondiscrete and
noncompact. We explore the ergodic theory of invariant point processes on G. Our first result …
noncompact. We explore the ergodic theory of invariant point processes on G. Our first result …
Invasion percolation on the Poisson-weighted infinite tree
L Addario-Berry, S Griffiths, RJ Kang - 2012 - projecteuclid.org
We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two
distinct Markovian representations of the resulting process. One of these is the σ→∞ limit of …
distinct Markovian representations of the resulting process. One of these is the σ→∞ limit of …
Rewriting History in Integrable Stochastic Particle Systems
Many integrable stochastic particle systems in one space dimension (such as TASEP—
Totally Asymmetric Simple Exclusion Process—and its q-deformation, the q-TASEP) remain …
Totally Asymmetric Simple Exclusion Process—and its q-deformation, the q-TASEP) remain …
The Palm groupoid of a point process and factor graphs on amenable and Property (T) groups
We define a probability measure preserving and r-discrete groupoid that is associated to
every invariant point process on a locally compact and second countable group. This …
every invariant point process on a locally compact and second countable group. This …
Ergodicity of Poisson products and applications
T Meyerovitch - 2013 - projecteuclid.org
In this paper we study the Poisson process over a σ-finite measure-space equipped with a
measure preserving transformation or a group of measure preserving transformations. For a …
measure preserving transformation or a group of measure preserving transformations. For a …
Indistinguishability of cells for the ideal Poisson Voronoi tessellation
In this note, we resolve a question of D'Achille, Curien, Enriquez, Lyons, and\" Unel by
showing that the cells of the ideal Poisson Voronoi tessellation are indistinguishable. This …
showing that the cells of the ideal Poisson Voronoi tessellation are indistinguishable. This …
Deterministic thinning of finite Poisson processes
Let $\Pi $ and $\Gamma $ be homogeneous Poisson point processes on a fixed set of finite
volume. We prove a necessary and sufficient condition on the two intensities for the …
volume. We prove a necessary and sufficient condition on the two intensities for the …