Related papers: Upper tail bounds for stationary KPZ models

Let $N$ be the number of triangles in an Erd\H{o}s-R\'enyi graph $\mathcal{G}(n,p)$ on $n$ vertices with edge density $p=d/n,$ where $d>0$ is a fixed constant. It is well known that $N$ weakly converges to the Poisson distribution with mean…

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

In this paper we give a conditional improvement to the Elekes-Szab\'{o} problem over the rationals, assuming the Uniformity Conjecture. Our main result states that for $F\in \mathbb{Q}[x,y,z]$ belonging to a particular family of…

The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and…

We obtain a probabilistic proof of the local Lipschitz continuity for the optimal stopping boundary of a class of problems with state space $[0,T]\times\mathbb{R}^d$, $d\ge 1$. To the best of our knowledge this is the only existing proof…

Under typical scaling, the last passage time field of the directed last passage percolation model with exponential site distributions converges to the KPZ fixed point. In this paper, we consider an atypical scenario in which the last…

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…

There is a renewed surge in percolation-induced transport properties of diverse nano-particle composites (cf. RSC Nanoscience & Nanotechnology Series, Paul O'Brien Editor-in-Chief). We note in particular a broad interest in nano-composites…

We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We…

Let $X$ be the number of $k$-term arithmetic progressions contained in the $p$-biased random subset of the first $N$ positive integers. We give asymptotically sharp estimates on the logarithmic upper-tail probability $\log \Pr(X \ge E[X] +…

In this paper, we consider the linearly reinforced and the once-reinforced random walk models in the transient phase on trees. We show the large deviations for the upper tails for both models. We also show the exponential decay for the…

Naslund used Tao's slice rank bounding method to give new exponential upper bounds for the Erd\H{o}s--Ginzburg-Ziv constant of finite Abelian groups of high rank. In our short manuscript we improve slightly Naslund's upper bounds. We extend…

We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance…

We discuss existence and stability of Riesz bases of exponential type of L^2(T) for special domains T called trapezoids. We construct exponential bases on L^2(T) when T is a finite union of rectangles with the same height. We also…

We prove upper bounds on the one-arm exponent $\eta_1$ for a class of dependent percolation models which generalise Bernoulli percolation; while our main interest is level set percolation of Gaussian fields, the arguments apply to other…

Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…

We prove that the ground state momentum distribution of a one-dimensional system of impenetrable bosons exhibits a $k^{-4}$ tail for any confining potential. We also derive an expression for easily computing the asymptotic occupation…

In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system.…

Consider the Hopf--Cole solution $ h(t,x) $ of the KPZ equation with narrow wedge initial condition. Regarding $ t\to\infty $ as a scaling parameter, we provide the first rigorous proof of the Large Deviation Principle (LDP) for the lower…