Asaf Nachmias

activity

20052026

most citedThe Alexander-Orbach conjecture holds in high dimensions

123 citations · 404 across the 40 of their papers we have counts for

collaborators

Showing math.PRShow all

42 papers · 1 filter

math.PR2025

Critical percolation on the discrete torus in high dimensions

Arthur Blanc-Renaudie, Asaf Nachmias

We consider percolation on the discrete torus $Z_{n}^{d}$ at $p_{c} (Z^{d})$ , the critical value for percolation on the corresponding infinite lattice $Z^{d}$ , and…

math.PR2025

Local limits of determinantal processes

Asaf Nachmias, Yuval Peled

Let $H_{n}$ be the row space of a signed adjacency matrix of a $C_{4}$ -free bipartite bi-regular graph in which one part has degree $d (n) \to \infty$ and the other part has degree $k + 1$ …

math.PR2025

Potentials in recurrent networks: a survey

Asaf Nachmias, Yuval Peres

A nonnegative function on the vertices of an infinite graph G which vanishes at a distinguished vertex o, has Laplacian 1 at o, and is harmonic at all other vertices is called a po…

math.PR2025

Every recurrent network has a potential tending to infinity

Asaf Nachmias, Yuval Peres

A rooted network consists of a connected, locally finite graph G, equipped with edge conductances and a distinguished vertex o. A nonnegative function on the vertices of G which va…

math.PR2024

The scaling limit of critical hypercube percolation

Arthur Blanc-Renaudie, Nicolas Broutin, Asaf Nachmias

We study the connected components in critical percolation on the Hamming hypercube ${0, 1}^{m}$ . We show that their sizes rescaled by $2^{- 2 m /3}$ converge in distribution, and that,…

math.PR2023

The union of independent USFs on $Z^{d}$ is transient

Eleanor Archer, Asaf Nachmias, Matan Shalev +1

We show that the union of two or more independent uniform spanning forests (USF) on $Z^{d}$ with $d \geq 3$ almost surely forms a connected transient graph. In fact, this als…

math.PR2022

The wired minimal spanning forest on the Poisson-weighted infinite tree

Asaf Nachmias, Pengfei Tang

We study the spectral and diffusive properties of the wired minimal spanning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). Let $M$ be the tree containing the root in…

math.PR2021

The GHP scaling limit of uniform spanning trees in high dimensions

Eleanor Archer, Asaf Nachmias, Matan Shalev

We show that the Brownian continuum random tree is the Gromov-Hausdorff-Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the $d$ -dimensional…

math.PR2020

The local limit of uniform spanning trees

Asaf Nachmias, Yuval Peres

We show that the local limit of the uniform spanning tree on any finite, simple, connected, regular graph sequence with degree tending to infinity is the Poisson(1) branching proce…

math.PR2020

The diameter of the uniform spanning tree of dense graphs

Noga Alon, Asaf Nachmias, Matan Shalev

We show that the diameter of a uniformly drawn spanning tree of a simple connected graph on $n$ vertices with minimal degree linear in $n$ is typically of order $n$ . A bypro…

math.PR2019★ 4 cited

The diameter of uniform spanning trees in high dimensions

Peleg Michaeli, Asaf Nachmias, Matan Shalev

We show that the diameter of a uniformly drawn spanning tree of a connected graph on $n$ vertices which satisfies certain high-dimensionality conditions typically grows like $Θ(\sq…

math.PR2019

The Dirichlet problem for orthodiagonal maps

Ori Gurel-Gurevich, Daniel C. Jerison, Asaf Nachmias

We prove that the discrete harmonic function corresponding to smooth Dirichlet boundary conditions on orthodiagonal maps, that is, plane graphs having quadrilateral faces with orth…

math.PR2019★ 4 cited

A combinatorial criterion for macroscopic circles in planar triangulations

Ori Gurel-Gurevich, Daniel C. Jerison, Asaf Nachmias

Given a finite simple triangulation, we estimate the sizes of circles in its circle packing in terms of Cannon's vertex extremal length. Our estimates provide control over the size…

math.PR2019★ 1 cited

Planar maps, random walks and circle packing

Asaf Nachmias

These are lecture notes of the 48th Saint-Flour summer school, July 2018, on the topic of planar maps, random walks and the circle packing theorem.

math.PR2017★ 9 cited

The local limit of the uniform spanning tree on dense graphs

Jan Hladký, Asaf Nachmias, Tuan Tran

Let $G$ be a connected graph in which almost all vertices have linear degrees and let $T$ be a uniform spanning tree of $G$ . For any fixed rooted tree $F$ of height $r$ we compute…

math.PR2017

Geometric and spectral properties of causal maps

Nicolas Curien, Tom Hutchcroft, Asaf Nachmias

We study the random planar map obtained from a critical, finite variance, Galton-Watson plane tree by adding the horizontal connections between successive vertices at each level. T…

math.PR2016★ 1 cited

Slightly subcritical hypercube percolation

Tim Hulshof, Asaf Nachmias

We study bond percolation on the hypercube ${0, 1}^{m}$ in the slightly subcritical regime where $p = p_{c} (1 - ε_{m})$ and $ε_{m} = o (1)$ but $\varepsilon_m \gg 2^{-m/…

math.PR2016

Hyperbolic and Parabolic Unimodular Random Maps

Omer Angel, Tom Hutchcroft, Asaf Nachmias +1

We show that for infinite planar unimodular random rooted maps, many global geometric and probabilistic properties are equivalent, and are determined by a natural, local notion of…

math.PR2016

Uniform Spanning Forests of Planar Graphs

Tom Hutchcroft, Asaf Nachmias

We prove that the free uniform spanning forest of any bounded degree proper plane graph is connected almost surely, answering a question of Benjamini, Lyons, Peres and Schramm. We…

math.PR2015★ 16 cited

Indistinguishability of Trees in Uniform Spanning Forests

Tom Hutchcroft, Asaf Nachmias

We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible…

math.PR2015★ 1 cited

Recurrence of multiply-ended planar triangulations

Ori Gurel-Gurevich, Asaf Nachmias, Juan Souto

In this note we show that a bounded degree planar triangulation is recurrent if and only if the set of accumulation points of some/any circle packing of it is polar (that is, plana…

math.PR2015★ 29 cited

Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk

Omer Angel, Tom Hutchcroft, Asaf Nachmias +1

We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation…

math.PR2014

Random walks on stochastic hyperbolic half planar triangulations

Omer Angel, Asaf Nachmias, Gourab Ray

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of…

math.PR2013★ 25 cited

Boundaries of planar graphs, via circle packings

Omer Angel, Martin T. Barlow, Ori Gurel-Gurevich +1

We provide a geometric representation of the Poisson and Martin boundaries of a transient, bounded degree triangulation of the plane in terms of its circle packing in the unit disc…

Critical percolation on the discrete torus in high dimensions

Local limits of determinantal processes

Potentials in recurrent networks: a survey

Every recurrent network has a potential tending to infinity

The scaling limit of critical hypercube percolation

The union of independent USFs on Zd is transient

The wired minimal spanning forest on the Poisson-weighted infinite tree

The GHP scaling limit of uniform spanning trees in high dimensions

The local limit of uniform spanning trees

The diameter of the uniform spanning tree of dense graphs

The diameter of uniform spanning trees in high dimensions

The Dirichlet problem for orthodiagonal maps

A combinatorial criterion for macroscopic circles in planar triangulations

Planar maps, random walks and circle packing

The local limit of the uniform spanning tree on dense graphs

Geometric and spectral properties of causal maps

Slightly subcritical hypercube percolation

Hyperbolic and Parabolic Unimodular Random Maps

Uniform Spanning Forests of Planar Graphs

Indistinguishability of Trees in Uniform Spanning Forests

Recurrence of multiply-ended planar triangulations

Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk

Random walks on stochastic hyperbolic half planar triangulations

Boundaries of planar graphs, via circle packings

The union of independent USFs on $Z^{d}$ is transient