Eviatar B. Procaccia

activity

20102026

most citedEigenvalue vs perimeter in a shape theorem for self-interacting random walks

11 citations · 75 across the 36 of their papers we have counts for

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34 papers · 1 filter

math.PR2026

Percolative MDLA: phase transition and critical behaviour

Eviatar B. Procaccia, Haoyu Wang, Yuan Zhang

In this paper we introduce the model of Percolative MDLA (PMDLA) on $Z^{2}$ which engulfs the entire occupied percolation component of each particle that reaches the aggrega…

math.PR2026

Cluster-Cluster model in $Z^{d}$

Noam Berger, Eviatar B. Procaccia, Dominik Schmid +1

We consider a stochastic process on $Z^{d}$ for $d \geq 1$ . Given a translation invariant and ergodic starting configuration of finite clusters, each cluster $C$ performs a…

math.PR2026

Pool model: a mass preserving multi particle aggregation process

Zhenhao Cai, Eviatar B. Procaccia, Yuan Zhang

We present and study the Pool model in $R^{2}$ , a rotationally symmetric analogue of Multi-Particle Diffusion-Limited Aggregation (MDLA), in which particles ("droplets") per…

math.PR2025

Chemical distance in graphs of polynomial growth

Christian Gorski, Eviatar B. Procaccia

We prove an Antal-Pisztora type theorem for transitive graphs of polynomial growth. That is, we show that if $G$ is a transitive graph of polynomial growth and $p > p_{c} (G)$ , then f…

math.PR2025

On one-dimensional Cluster cluster model

Noam Berger, Eviatar B. Procaccia, Daniel Sharon

The Cluster-cluster model was introduced by Meakin et al in 1984. Each $x \in Z^{d}$ starts with a cluster of size 1 with probability $p \in (0, 1]$ independently. Each cluste…

math.PR2025

One-arm domination time in Cylindrical Hastings-Levitov $(0)$

Guanyi Chen, Eviatar B. Procaccia, Yuxuan Zong

The cylindrical Hastings-Levitov $(0)$ admits a single infinite connected tree (arm). For a cylinder of width $N$ and particles of size $λ$ , {we consider the first time $\upsilon_{N…

math.PR2025

Logarithmic fluctuations of Stationary Hastings-Levitov

Noam Berger, Eviatar B. Procaccia

We prove that the fluctuation field ${M_{t} (x)}_{x \in R}$ of stationary Hastings-Levitov $(0)$ exhibits logarithmic spatial correlations. Moreover, by studying the infinites…

math.PR2024

Minimal harmonic measure on 2D lattices

Zhenhao Cai, Eviatar B. Procaccia, Yuan Zhang

We study the harmonic measure (i.e. the limit of the hitting distribution of a simple random walk starting from a distant point) on three canonical two-dimensional lattices: the sq…

math.PR2023

Vertex-removal stability and the least positive value of harmonic measures

Zhenhao Cai, Gady Kozma, Eviatar B. Procaccia +1

We prove that for $Z^{d}$ ( $d \geq 2$ ), the vertex-removal stability of harmonic measures (i.e. it is feasible to remove some vertex while changing the harmonic measure by a b…

math.PR2023

Cylindrical Hastings Levitov

Eviatar B. Procaccia, Anna Zhuchenko

We define a Hastings-Levitov $(0)$ process on a cylinder and prove that the process converges to Stationary Hastings Levitov $(0)$ under appropriate particle size scaling that depend…

math.PR2022

A toy model for DLA arm growth in a wedge

Oren Louidor, Chanwoo Oh, Eviatar B. Procaccia

In this paper, we consider a non-homogeneous discrete-time Markov chain which can be seen as a toy model for the growth of the arms of the DLA (Diffusion limited aggregation) proce…

math.PR2021★ 1 cited

The chemical distance in random interlacements in the low-intensity regime

Sarai Hernandez-Torres, Eviatar B. Procaccia, Ron Rosenthal

In $Z^{d}$ with $d \geq 5$ , we consider the time constant $ρ_{u}$ associated to the chemical distance in random interlacements at low intensity $u ≪ 1$ . We prove an upper boun…

math.PR2021

Continuity and uniqueness of percolation critical parameters in Finitary Random Interlacements

Zhenhao Cai, Eviatar B. Procaccia, Yuan Zhang

We prove that the critical percolation parameter for Finitary Random Interlacements (FRI) is continuous with respect to the path length parameter $T$ . The proof uses a result which…

math.PR2020★ 9 cited

Growth of Stationary Hastings-Levitov

Noam Berger, Eviatar B. Procaccia, Amanda Turner

We construct and study a stationary version of the Hastings-Levitov $(0)$ model. We prove that, unlike in the classical HL $(0)$ model, in the stationary case the size of particles a…

math.PR2019★ 1 cited

Scaling limit of DLA on a long line segment

Yingxin Mu, Eviatar B. Procaccia, Yuan Zhang

In this paper, we prove that the bulk of DLA starting from a long line segment on the $x$ -axis has a scaling limit to the stationary DLA process (SDLA). The main phenomenological d…

math.PR2019★ 3 cited

Percolation for the Finitary Random interlacements

Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang

In this paper, we prove a phase transition in the connectivity of Finitary Random interlacements $F I^{u, T}$ in $Z^{d}$ , with respect to the average stopping time.…

math.PR2019★ 8 cited

Stationary DLA is well defined

Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang

In this paper, we construct an infinite stationary Diffusion Limited Aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate prop…

math.PR2018★ 5 cited

Stationary Harmonic Measure as the Scaling Limit of Truncated Harmonic Measure

Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang

In this paper we prove that the stationary harmonic measure of an infinite set in the upper planar lattice can be represented as the proper scaling limit of the classical harmonic…

math.PR2018

Stabilization of DLA in a wedge

Eviatar B. Procaccia, Ron Rosenthal, Yuan Zhang

We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $π /4$ , there is some $a > 2$ such that almost sure…

math.PR2017★ 2 cited