Related papers: Sub-exponential tail bounds for conditioned stable…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We show, under natural conditions, that uniform rooted trees with fixed degree sequence converge after renormalization toward inhomogeneous continuum random trees (ICRT). We also provide a sharp upper-bound for the tail of their heights. We…
We consider a fragmentation of discrete trees where the internal vertices are deleted independently at a rate proportional to their degree. Informally, the associated cut-tree represents the genealogy of the nested connected components…
The well-known "Janson's inequality" gives Poisson-like upper bounds for the lower tail probability \Pr(X \le (1-\eps)\E X) when X is the sum of dependent indicator random variables of a special form. We show that, for large deviations,…
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…
Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued…
We study several parameters of a random Bienaym\'e-Galton-Watson tree $T_n$ of size $n$ defined in terms of an offspring distribution $\xi$ with mean $1$ and nonzero finite variance $\sigma^2$. Let $f(s)={\bf E}\{s^\xi\}$ be the generating…
We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of…
We consider Galton--Watson trees conditioned on both the total number of vertices $n$ and the number of leaves $k$. The focus is on the case in which both $k$ and $n$ grow to infinity and $k = \alpha n + O(1)$, with $\alpha \in (0, 1)$.…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
Although there is an extensive literature on the maxima of Gaussian processes, there are relatively few non-asymptotic bounds on their lower-tail probabilities. The aim of this paper is to develop such a bound, while also allowing for many…
There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an…
We consider critical percolation on a supercritical Galton-Watson tree. We show that, when the offspring distribution is in the domain of attraction of an $\alpha$-stable law for some $\alpha \in (1,2)$, or has finite variance, several…
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the…
We investigate the effective resistance $R_n$ and conductance $C_n$ between the root and leaves of a binary tree of height $n$. In this electrical network, the resistance of each edge $e$ at distance $d$ from the root is defined by…
In this work, we study asymptotics of the genealogy of Galton--Watson processes conditioned on the total progeny. We consider a fixed, aperiodic and critical offspring distribution such that the rescaled Galton--Watson processes converges…
An explicit upper bound on the tail probabilities for the normalized Rademacher sums is given. This bound, which is best possible in a certain sense, is asymptotically equivalent to the corresponding tail probability of the standard normal…
In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…