Related papers: Heavy tails in last-passage percolation

As well known, for a supercritical Galton-Watson process $Z_n$ whose offspring distribution has mean $m>1$, the ratio $W_n:=Z_n/m^n$ has a.s. limit, say $W$. We study tail behaviour of the distributions of $W_n$ and $W$ in the case where…

This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…

We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.

This paper addresses the problem of estimating the tail index of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A…

We consider planar stationary exponential Last Passage Percolation in the positive quadrant with boundary weights. For $\rho\in (0,1)$ and points $v_N=((1-\rho)^2 N,\rho^2 N)$ going to infinity along the characteristic direction, we…

We study line ensembles arising naturally in symmetrized/half-space geometric last passage percolation (LPP) on the $N \times N$ square. The weights of the model are geometrically distributed with parameter $q^2$ off the diagonal and $cq$…

We introduce and study a model of directed last-passage percolation in planar layered environment. This environment is represented by an array of random exponential clocks arranged in blocks, for each block the average waiting times depend…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical…

We propose another proof of the high dimensional spectrum convergence of the weighted sample covariance, more concise and self-sufficient but with stronger, but reasonable assumptions. We explain and illustrates this theorem for different…

In this paper we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times with scaling exponent 3/2, and we…

We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary of the quadrant, but may have unbounded jumps in the opposite direction,…

We provide Monte Carlo estimates of the scaling of the length $L_{n}$ of the longest increasing subsequences of $n$-steps random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate…

Consider $n$ i.i.d. random vectors on $\mathbb{R}^2$, with unknown, common distribution function $F$. Under a sharpening of the extreme value condition on $F$, we derive a weighted approximation of the corresponding tail copula process.…

A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be…

This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…

We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged…

For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…

A well-known question in planar first-passage percolation concerns the convergence of the empirical distribution of weights as seen along geodesics. We demonstrate this convergence for an explicit model, directed last-passage percolation on…