Barbara Dembin

Sharpness for monotone absorbing Interacting Particle Systems

Jean Bérard, Barbara Dembin, Laure Marêché

We prove a sharpness result for the dynamics of finite-range Interacting Particle Systems (IPS) on ${0, 1}^{Z^{d}}$ , which generalizes to a whole class of IPS the sharpness result…

Noise sensitivity and variance lower bound for minimal left-right crossing of a square in first-passage percolation

Barbara Dembin, Dor Elboim

We study first-passage percolation on $Z^{2}$ with independent and identically distributed weights, whose common distribution is uniform on ${a, b}$ with $0 < a < b < \infty$ . F…

Minimal surfaces in strongly correlated random environments

Barbara Dembin, Dor Elboim, Ron Peled

A minimal surface in a random environment (MSRE) is a $d$ -dimensional surface in $(d + n)$ -dimensional space which minimizes the sum of its elastic energy and its environment potenti…

High-intensity Voronoi percolation on manifolds

Tillmann Bühler, Barbara Dembin, Ritvik Ramanan Radhakrishnan +1

We study Voronoi percolation on a large class of $d$ -dimensional Riemannian manifolds, which includes the hyperbolic spaces $H^{d}$ , $d \geq 2$ . We prove that as the intensit…

math-ph2024

Minimal surfaces in random environment

Barbara Dembin, Dor Elboim, Daniel Hadas +1

A minimal surface in a random environment (MSRE) is a surface which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary con…

Supercritical sharpness for Voronoi percolation

Barbara Dembin, Franco Severo

We prove that the supercritical phase of Voronoi percolation on $R^{d}$ , $d \geq 3$ , is well behaved in the sense that for every $p > p_{c} (d)$ local uniqueness of macroscopic cl…

On the influence of edges in first-passage percolation on $Z^{d}$

Barbara Dembin, Dor Elboim, Ron Peled

We study first-passage percolation on $Z^{d}$ , $d \geq 2$ , with independent weights whose common distribution is compactly supported in $(0, \infty)$ with a uniformly-positive d…

Superconcentration for minimal surfaces in first passage percolation and disordered Ising ferromagnets

Barbara Dembin, Christophe Garban

We consider the standard first passage percolation model on $Z^{d}$ with a distribution $G$ taking two values $0 < a < b$ . We study the maximal flow through the cylinder $[0,n]^…

Subcritical sharpness for multiscale Boolean percolation

Barbara Dembin

We consider a multiscale Boolean percolation on $R^{d}$ with radius distribution $μ$ on $[1, + \infty)$ , $d \geq 2$ . The model is defined by superposing the original Boolean perc…

math.PR2022

On the upper tail large deviation rate function for chemical distance in supercritical percolation

Barbara Dembin, Shuta Nakajima

We consider the supercritical bond percolation on $Z^{d}$ and study the graph distance on the percolation graph called the chemical distance. It is well-known that there exis…

math.PR2022

Almost sharp sharpness for Poisson Boolean percolation

Barbara Dembin, Vincent Tassion

We consider Poisson Boolean percolation on $R^{d}$ with power-law distribution on the radius with a finite $d$ -moment for $d \geq 2$ . We prove that subcritical sharpness occurs…

math.PR2022

Coalescence of geodesics and the BKS midpoint problem in planar first-passage percolation

Barbara Dembin, Dor Elboim, Ron Peled

We consider first-passage percolation on $Z^{2}$ with independent and identically distributed weights whose common distribution is absolutely continuous with a finite exponen…

math.PR2022★ 1 cited

The variance of the graph distance in the infinite cluster of percolation is sublinear

Barbara Dembin

We consider the standard model of i.i.d. bond percolation on $Z^{d}$ of parameter $p$ . When $p > p_{c}$ , there exists almost surely a unique infinite cluster $C_{p}$ . Usin…

math.PR2021★ 2 cited

Large deviation principle for the cutsets and lower large deviation principle for the maximal flow in first passage percolation

Barbara Dembin, Marie Théret

We consider the standard first passage percolation model in the rescaled lattice $Z^{d} / n$ for $d \geq 2$ and a bounded domain $Ω$ in $R^{d}$ . We denote by $Γ^{1}$ and $Γ^…

math.PR2021

The time constant for Bernoulli percolation is Lipschitz continuous strictly above $p_{c}$

Raphaël Cerf, Barbara Dembin

We consider the standard model of i.i.d. first passage percolation on $Z^{d}$ given a distribution $G$ on $[0, + \infty]$ ( $+ \infty$ is allowed). When $G([0,+\infty]) < p_c(d)…

math.PR2020★ 1 cited

Large deviation principle for the streams and the maximal flow in first passage percolation

Barbara Dembin, Marie Théret

We consider the standard first passage percolation model in the rescaled lattice $Z^{d}$ for $d \geq 2$ and a bounded domain $Ω$ in $R^{d}$ . We denote by $Γ^{1}$ and $Γ^…

math.PR2019

Vanishing of the anchored isoperimetric profile in bond percolation at p c

Raphaël Cerf, Barbara Dembin

We consider the anchored isoperimetric profile of the infinite open cluster, defined for $p > p_c$ , whose existence has been recently proved in [3]. We extend adequately the defin…

Anchored isoperimetric profile of the infinite cluster in supercritical bond percolation is Lipschitz continuous

Barbara Dembin

We consider an i.i.d. supercritical bond percolation on $Z^{d}$ , every edge is open with a probability $p > p_{c} (d)$ , where $p_{c} (d)$ denotes the critical parameter for this…

Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher

Barbara Dembin

Let $d \geq 2$ . We consider an i.i.d. supercritical bond percolation on $Z^{d}$ , every edge is open with a probability $p > p_{c} (d)$ , where $p_{c} (d)$ denotes the critical point.…

The maximal flow from a compact convex subset to infinity in first passage percolation on Z^d

Barbara Dembin

We consider the standard first passage percolation model on Z^d with a distribution G on R+ that admits an exponential moment. We study the maximal flow between a compact convex su…