228 citations · 583 across the 35 of their papers we have counts for
35 papers · 1 filter
Scaling limits for random walks on long range percolation clusters
Noam Berger, Yuki Tokushige
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two…
Doeblin measures: uniqueness and mixing properties
Noam Berger, Diana Conache, Anders Johannson +1
In this paper we solve two open problems in ergodic theory. We prove first that if a Doeblin function (a -function) satisfies \[\limsup_{n\to\infty}\frac{\mbox{var}_n \log g…
Isoperimetric lower bounds for critical exponents for long-range percolation
Johannes Bäumler, Noam Berger
We study independent long-range percolation on where the vertices and are connected with probability for . Provided the critic…
A parabolic Harnack principle for balanced difference equations in random environments
Noam Berger, David Criens
We consider difference equations in balanced, i.i.d. environments which are not necessary elliptic. In this setting we prove a parabolic Harnack inequality (PHI) for non-negative s…
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…
An elliptic Harnack inequality for random walk in balanced environments
Noam Berger, Moran Cohen, Jean-Dominique Deuschel +1
We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation…
The speed of biased random walk among random conductances
Noam Berger, Nina Gantert, Jan Nagel
We consider biased random walk among iid, uniformly elliptic conductances on , and investigate the monotonicity of the velocity as a function of the bias. It is not h…
Quenched large deviations for simple random walks on percolation models including long-range correlations
Noam Berger, Chiranjib Mukherjee, Kazuki Okamura
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on (). The models under in…
Quenched Large Deviations for Simple Random Walks on Supercritical Percolation Clusters
Noam Berger, Chiranjib Mukherjee
We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster on , .. We take the point of view of the m…
Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments
Noam Berger, Moran Cohen, Ron Rosenthal
In this work, we discuss certain ballistic random walks in random environments on , and prove the equivalence between the static and dynamic points of view in dimensi…
Asymptotic behavior and distributional limits of preferential attachment graphs
Noam Berger, Christian Borgs, Jennifer T. Chayes +1
We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations tha…
Zero-one law for directional transience of one dimensional excited random walks
Gideon Amir, Noam Berger, Tal Orenshtein
The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves…
Mutually excited random walks
Noam Berger, Eviatar B. Procaccia
Consider two random walks on . The transition probabilities of each walk is dependent on trajectory of the other walker i.e. a drift is obtained in a position t…
Detecting the trail of a random walker in a random scenery
Noam Berger, Yuval Peres
Suppose that the vertices of the Euclidean lattice Z^d are endowed with a random scenery, obtained by tossing a fair coin at each vertex. A random walker, starting from the origin,…
Stretch IDLA
Noam Berger, Jacob J. Kagan, Eviatar B. Procaccia
We consider a new IDLA - particle system model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. We prove that almost surely all trees are…
Effective Polynomial Ballisticity Condition for Random Walk in Random Environment
Noam Berger, Alexander Drewitz, Alejandro F. Ramírez
The conditions which have been introduced by Sznitman in 2002, have had a significant impact on research in random walk in random environment. Among others,…
On the speed of Random Walks among Random Conductances
Noam Berger, Michele Salvi
We consider random walk among random conductances where the conductance environment is shift invariant and ergodic. We study which moment conditions of the conductances guarantee s…
Behavior of random walk on discrete point processes
Noam Berger, Ron Rosenthal
We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nea…
A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment
Noam Berger, Jean-Dominique Deuschel
We consider a random walk on Z^d in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x to nearest neighbor x+e is the same as to…
Random walk on discrete point processes
Ron Rosenthal
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities o…
Ballisticity conditions for random walk in random environment
Alexander Drewitz, Alejandro F. Ramírez
Consider a random walk in a uniformly elliptic i.i.d. random environment in dimensions . In 2002, Sznitman introduced for each the ballisticity conditions $(T)…
Slowdown estimates for ballistic random walk in random environment
Noam Berger
For a random walk in an elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying the a ballisticity condition slightly weaker than condition (T'), We…
Long Range Percolation Mixing Time
Itai Benjamini, Noam Berger, Ariel Yadin
We provide an estimate, sharp up to poly-logarithmic factors, of the asymptotically almost sure mixing time of the graph created by long-range percolation on the cycle of length N…
A quenched invariance principle for certain ballistic random walks in i.i.d. environments
Noam Berger, Ofer Zeitouni
We prove that every random walk in i.i.d. environment in dimension greater than or equal to 2 that has an almost sure positive speed in a certain direction, an annealed invariance…