11 citations · 75 across the 36 of their papers we have counts for
40 papers
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 which engulfs the entire occupied percolation component of each particle that reaches the aggrega…
Cluster-Cluster model in
Noam Berger, Eviatar B. Procaccia, Dominik Schmid +1
We consider a stochastic process on for . Given a translation invariant and ergodic starting configuration of finite clusters, each cluster performs a…
Pool model: a mass preserving multi particle aggregation process
Zhenhao Cai, Eviatar B. Procaccia, Yuan Zhang
We present and study the Pool model in , a rotationally symmetric analogue of Multi-Particle Diffusion-Limited Aggregation (MDLA), in which particles ("droplets") per…
A New Probabilistic Mobile Byzantine Failure Model for Self-Protecting Systems
Silvia Bonomi, Giovanni Farina, Roy Friedman +2
Modern distributed systems face growing security threats, as attackers continuously enhance their skills and vulnerabilities span across the entire system stack, from hardware to t…
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 is a transitive graph of polynomial growth and , then f…
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 starts with a cluster of size 1 with probability independently. Each cluste…
One-arm domination time in Cylindrical Hastings-Levitov
Guanyi Chen, Eviatar B. Procaccia, Yuxuan Zong
The cylindrical Hastings-Levitov admits a single infinite connected tree (arm). For a cylinder of width and particles of size , {we consider the first time $\upsilon_{N…
Logarithmic fluctuations of Stationary Hastings-Levitov
Noam Berger, Eviatar B. Procaccia
We prove that the fluctuation field of stationary Hastings-Levitov exhibits logarithmic spatial correlations. Moreover, by studying the infinites…
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…
The Double Bubble Problem in the Hexagonal Norm
Parker Duncan, Rory O'Dwyer, Eviatar B. Procaccia
We study the double bubble problem where the perimeter is taken with respect to the hexagonal norm, i.e. the norm whose unit circle in is the regular hexagon. We pro…
Vertex-removal stability and the least positive value of harmonic measures
Zhenhao Cai, Gady Kozma, Eviatar B. Procaccia +1
We prove that for (), the vertex-removal stability of harmonic measures (i.e. it is feasible to remove some vertex while changing the harmonic measure by a b…
Cylindrical Hastings Levitov
Eviatar B. Procaccia, Anna Zhuchenko
We define a Hastings-Levitov process on a cylinder and prove that the process converges to Stationary Hastings Levitov under appropriate particle size scaling that depend…
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…
The chemical distance in random interlacements in the low-intensity regime
Sarai Hernandez-Torres, Eviatar B. Procaccia, Ron Rosenthal
In with , we consider the time constant associated to the chemical distance in random interlacements at low intensity . We prove an upper boun…
Discrete Double Bubble solution is at most ceiling +2 of the continuous solution
Parker Duncan, Rory O'Dwyer, Eviatar B. Procaccia
In this paper we show that the solution of the discrete Double Bubble problem over is at most the ceiling function plus two of the continuous solution to the Double…
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 . The proof uses a result which…
An elementary proof for the Double Bubble problem in norm
Parker Duncan, Rory O'Dwyer, Eviatar B. Procaccia
We study the double bubble problem with perimeter taken with respect to the norm on . We give an elementary proof for the existence of minimizing sets for an…
Growth of Stationary Hastings-Levitov
Noam Berger, Eviatar B. Procaccia, Amanda Turner
We construct and study a stationary version of the Hastings-Levitov model. We prove that, unlike in the classical HL model, in the stationary case the size of particles a…
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 -axis has a scaling limit to the stationary DLA process (SDLA). The main phenomenological d…
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 in , with respect to the average stopping time.…
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…
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…
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 , there is some such that almost sure…
Stationary Harmonic Measure and DLA in the Upper half Plane
Eviatar B. Procaccia, Yuan Zhang
In this paper, we introduce the stationary harmonic measure in the upper half plane. By bounding this measure, we are able to define both the discrete and continuous time diffusion…