Related papers: Superconcentration and chaos in Bernoulli percolat…
Considering supercritical Bernoulli percolation on $\mathbb{Z}^d$, Garet and Marchand [GM09] proved a diffusive concentration for the graph distance. In this paper, we sharpen this result by establishing the subdiffusive concentration…
We identify the asymptotic distribution of the chemical distance in high-dimensional critical Bernoulli percolation. Namely, we show that the distance between the origin and a distant vertex conditioned to lie in the cluster of the origin…
The aim of this paper is to generalize the well-known asymptotic shape result for first-passage percolation on $\Zd$ to first-passage percolation on a random environment given by the infinite cluster of a supercritical Bernoulli percolation…
For directed Bernoulli last passage percolation with i.i.d.~weights on vertices over a $n\times n$ grid and for $n$ large enough, the geodesics are shown to be concentrated in a cylinder, centered on the main diagonal and of width of order…
We prove that, the diffusivity and conductivity on $\mathbb{Z}^d$-Bernoulli percolation ($d \geq 2$) are infinitely differentiable in supercritical regime. This extends a result by Kozlov [Uspekhi Mat. Nauk 44 (1989), no. 2(266), pp 79 -…
In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance between two points is the length of the shortest open path between these two points. Thus, we study the size of random…
In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance between two points is the length of the shortest open path between these two points. Thus, we study the size of random…
Gaussian percolation can be seen as the generalization of standard Bernoulli percolation on $\mathbb{Z}^d$. Instead of a random discrete configuration on a lattice, we consider a continuous Gaussian field $f$ and we study the topological…
First-passage percolation is the study of the metric space $(\mathbb{Z}^d,T)$, where $T$ is a random metric defined as the weighted graph metric using random edge-weights $(t_e)_{e\in \mathcal{E}^d}$ assigned to the nearest-neighbor edges…
We consider a superfluid state in a two-component gas of fermionic atoms with equal densities and unequal masses in the BCS limit. We develop a perturbation theory along the lines proposed by Gorkov and Melik-Barkhudarov and find that for a…
We show quenched large deviations for the simple random walk on a certain class of percolations with long-range correlations. This class contains the supercritical Bernoulli percolations, the model considered by Drewitz, R'ath and…
The chemical distance D(x,y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behaviour of this random metric, and we prove that, for an…
We show that a superposition of an $\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\mathbb Z^d$, $d\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli…
In this paper we provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distances, focusing…
In this paper, we consider Bernoulli percolation on a locally finite, transitive and infinite graph (e.g. the hypercubic lattice $\mathbb{Z}^d$). We prove the following estimate, where $\theta_n(p)$ is the probability that there is a path…
A decade and a half ago Chatterjee established the first rigorous connection between anomalous fluctuations and a chaotic behaviour of the ground state in certain Gaussian disordered systems. The purpose of this paper is to show that…
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 percolation. We know that there exists almost surely a unique infinite…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
The physics of quantum degenerate Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions which play a crucial role, bringing the…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…