Related papers: Upper tail large deviations of the directed landsc…
In this paper, we study lower tail probabilities of the height function $\mathfrak{h}(M,N)$ of the stochastic six-vertex model. We introduce a novel combinatorial approach to demonstrate that the tail probabilities…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…
We establish a large deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, the large deviation principle is derived for super-Brownian…
In this paper, we study large time large deviations for the height function $\mathfrak{h}(x,t)$ of the $q$-deformed polynuclear growth introduced in ABW22 [arXiv:2108.06018]. We show that the upper-tail deviations have speed $t$ and derive…
We consider a multivariate distributional recursion of sum-type as arising in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the…
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…
We present a large deviation principle at speed N for the largest eigenvalue of some additively deformed Wigner matrices. In particular this includes Gaussian ensembles with full-rank general deformation. For the non-Gaussian ensembles, the…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classical Wentzel--Freidlin theorem, but under the considerably…
We prove large deviation results for the position of the rightmost particle, denoted by $M_n$, in a one-dimensional branching random walk in a case when Cram\'er's condition is not satisfied. More precisely we consider step size…
The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric,…
Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property…
We prove that the random variable $\ct=\argmax_{t\in\rr}\{\aip(t)-t^2\}$ has tails which decay like $e^{-ct^3}$. The distribution of $\ct$ is a universal distribution which governs the rescaled endpoint of directed polymers in 1+1…
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…
In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle…
Large-deviation upper bounds on compact sets do not, in general, extend to arbitrary closed sets without additional tightness. We show that this obstruction already occurs in static entropic optimal transport. More precisely, we construct a…
For models in the KPZ universality class, such as the zero temperature model of planar last passage-percolation (LPP) and the positive temperature model of directed polymers, its upper tail behavior has been a topic of recent interest, with…