15 citations · 38 across the 14 of their papers we have counts for
16 papers
On Stopping Sets and Continuous-Time Decision Trees
Ali Khezeli
We study stopping sets and continuous-time decision trees (CTDTs) for Poisson point processes. We prove that every -continuous CTDT has an explicit exploration representation: b…
Convergence towards Ideal Poisson--Voronoi tessellations with a focus on Diestel--Leader graphs
Matteo D'Achille, Ali Khezeli
We provide necessary and sufficient conditions for convergence towards a unique IPVT on any proper pointed measured metric space. The conditions are that the volume function, when…
Indistinguishability in One-or-Two-Ended Forests on Unimodular Random Graphs
Francois Baccelli, Ali Khezeli
Indistinguishability is a form of ergodicity, introduced by Lyons and Schramm for percolation clusters, that has become a fundamental notion in the theory of random infinite graphs…
Vanishing uniqueness thresholds in Voronoi percolation on products
Matteo D'Achille, Jan Grebík, Ali Khezeli +2
We study Poisson--Voronoi percolation and its discrete analogue Bernoulli--Voronoi percolation in spaces with a non-amenable product structure. We develop a new method of proving s…
Products of Infinite Countable Groups Have Fixed Price One
Ali Khezeli
We prove that the product of any two infinite countable groups has fixed price one. This resolves a longstanding problem posed by Gaboriau. The proof uses the propagation method to…
Unimodular Random Measured Metric Spaces and Palm Theory on Them
Ali Khezeli
In this work, we define the notion of unimodular random measured metric spaces as a common generalization of various other notions. This includes the discrete cases like unimodular…
On the Existence of Balancing Allocations and Factor Point Processes
Ali Khezeli, Samuel Mellick
In this article, we show that every stationary random measure on that is essentially free (i.e., has no symmetries a.s.) admits a point process as a factor (i.e., as…
An Improved Lower Bound on the Largest Common Subtree of Random Leaf-Labeled Binary Trees
Ali Khezeli
It is known that the size of the largest common subtree (i.e., the maximum agreement subtree) of two independent random binary trees with given labeled leaves is of order betwe…
Counter Examples to Invariant Circle Packing
Ali Khezeli
In this work, a unimodular random planar triangulation is constructed that has no invariant circle packing. This disputes a problem asked in [arXiv:1910.01614]. A natural weaker pr…
Metrization of the Gromov-Hausdorff (-Prokhorov) Topology for Boundedly-Compact Metric Spaces
Ali Khezeli
In this work, a metric is presented on the set of boundedly-compact pointed metric spaces that generates the Gromov-Hausdorff topology. A similar metric is defined for measured met…
A Unified Framework for Generalizing the Gromov-Hausdorff Metric
Ali Khezeli
In this paper, an approach for generalizing the Gromov-Hausdorff metric is presented, which applies to metric spaces equipped with some additional structure. A special case is the…
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…
Shift-Coupling of Random Rooted Graphs and Networks
Ali Khezeli
In this paper, we present a result similar to the shift-coupling result of Thorisson (1996) in the context of random graphs and networks. The result is that a given random rooted n…
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…
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…