相关论文: A modified Poincare inequality and its application…

The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…

We prove that, under the condition of validity of the Fresnel approximation, diffraction and interference for a wave traveling in the z-direction may be described in terms of the spreading in time of the transverse (x,y)-wave packet. The…

Consider the first passage percolation model on ${\bf Z}^d$ for $d\geq 2$. In this model we assign independently to each edge the value zero with probability $p$ and the value one with probability $1-p$. We denote by $T({\bf 0}, v)$ the…

This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincar\'e and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo-Nirenberg-Sobolev…

We introduce a new notion of influence for symmetric convex sets over Gaussian space, which we term "convex influence". We show that this new notion of influence shares many of the familiar properties of influences of variables for monotone…

We characterize the real interpolation space between weighted $L^1$ and $W^{1,1}$ spaces on arbitrary domains different from $\mathbb{R}^n$, when the weights are positive powers of the distance to the boundary multiplied by an $A_1$ weight.…

Weighted Poincar\'e-type and related inequalities provide upper bounds of the variance of functions. Their application in sensitivity analysis allows for quickly identifying the active inputs. Although the efficiency in prioritizing inputs…

This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit…

A law of the iterated logarithm is established for the last passage times of directed percolation on rectangles in the plane over exponential or geometric independent random variables, rescaled to converge to the Tracy-Widom distribution.…

We study the problem of coexistence in a two-type competition model governed by first-passage percolation on $\Zd$ or on the infinite cluster in Bernoulli percolation. Actually, we prove for a large class of ergodic stationary passage times…

We study first passage percolation on the configuration model. Assuming that each edge has an independent exponentially distributed edge weight, we derive explicit distributional asymptotics for the minimum weight between two randomly…

Let $\mathbb{G}=\left(\mathbb{V},\mathbb{E}\right)$ be the graph obtained by taking the cartesian product of an infinite and connected graph $G=(V,E)$ and the set of integers $\mathbb{Z}$. We choose a collection $\mathcal{C}$ of finite…

We consider the following oriented percolation model of $\mathbb {N} \times \mathbb{Z}^d$: we equip $\mathbb {N}\times \mathbb{Z}^d$ with the edge set $\{[(n,x),(n+1,y)] | n\in \mathbb {N}, x,y\in \mathbb{Z}^d\}$, and we say that each edge…

This note is concerned with lower tail estimates for product measures. Some improved deviation inequalities are obtained for functions satisfying some regularity and monotonicity assumptions. The arguments are based on semigroup…

This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…

We consider first-passage percolation on a ladder, i.e. the graph {0,1,...}*{0,1} where nodes at distance 1 are joined by an edge, and the times are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to calculate an…

In exponential last passage percolation, we consider the rescaled Busemann process $x\mapsto N^{-1/3}B^\rho_{0,[xN^{2/3}]e_1} \,\, (x\in\mathbb{R})$, as a process parametrized by the scaled density $\rho=1/2+\frac{\mu}{4} N^{-1/3}$, and…

We consider first passage percolation on the Erd\H{o}s--R\'{e}nyi graph with $n$ vertices in which each pair of distinct vertices is connected independently by an edge with probability $\lambda/n$ for some $\lambda>1$. The edges of the…

We consider a model of first passage percolation (FPP) where the nearest-neighbor edges of the standard two-dimensional Euclidean lattice are equipped with random variables. These variables are i.i.d.\, nonnegative, continuous, and have a…

First passage under restart with branching is proposed as a generalization of first passage under restart. Strong motivation to study this generalization comes from the observation that restart with branching can expedite the completion of…