21 citations · 42 across the 5 of their papers we have counts for
9 papers
Coupling from the Past for the Null Recurrent Markov Chain
François Baccelli, Mir-Omid Haji-Mirsadeghi, Sayeh Khaniha
The Doeblin Graph of a countable state space Markov chain describes the joint pathwise evolutions of the Markov dynamics starting from all possible initial conditions, with two pat…
Doeblin Trees
François Baccelli, Mir-Omid Haji-Mirsadeghi, James T. Murphy
This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This…
Unimodular Billingsley and Frostman Lemmas
François Baccelli, Mir-Omid Haji-Mirsadeghi, Ali Khezeli
The notions of unimodular Minkowski and Hausdorff dimensions are defined in [arXiv:1807.02980] for unimodular random discrete metric spaces. The present paper is focused on the con…
Unimodular Hausdorff and Minkowski Dimensions
François Baccelli, Mir-Omid Haji-Mirsadeghi, Ali Khezeli
This work introduces two new notions of dimension, namely the unimodular Minkowski and Hausdorff dimensions, which are inspired from the classical analogous notions. These dimensio…
Eternal Family Trees and Dynamics on Unimodular Random Graphs
François Baccelli, Mir-Omid Haji-Mirsadeghi, Ali Khezeli
This paper is centered on covariant dynamics on unimodular random graphs and random networks, namely maps from the set of vertices to itself which are preserved by graph or network…
Point-Shift Foliation of a Point Process
François Baccelli, Mir-Omid Haji-Mirsadeghi
A point-shift maps each point of a point process to some point of . For all translation invariant point-shifts , the -foliation of is a partition of the suppor…
Stable transports between stationary random measures
Mir-Omid Haji-Mirsadeghi, Ali Khezeli
We give an algorithm to construct a translation-invariant transport kernel between ergodic stationary random measures and on , given that they have equal inten…
Point-Map-Probabilities of a Point Process and Mecke's Invariant Measure Equation
François Baccelli, Mir-Omid Haji-Mirsadeghi
A compatible point-shift maps, in a translation invariant way, each point of a stationary point process to some point of . It is fully determined by its associated point…
Optimal Paths on the Space-Time SINR Random Graph
Francois Baccelli, Bartlomiej Blaszczyszyn, Mir Omid Haji Mirsadeghi
We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast…