Related papers: Right-tail moderate deviations in the exponential …
Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative…
We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…
We study the random conductance model on the lattice $\Z^d$, i.e. we consider a linear, finite-difference, divergence-form operator with random conductances $a$. We allow the conductances $a$ to be unbounded and degenerate. Assuming the…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
Considered are the large $N$, or large intensity, forms of the distribution of the length of the longest increasing subsequences for various models. Earlier work has established that after centring and scaling, the limit laws for these…
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…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…
We consider extremal processes and random walks generated by heavy-tailed random vectors taking values in $\mathbb{R}^d$ endowed with the $\ell_p$ metric. We establish limit theorems for the associated paths in the triangular array setting…
For exactly solvable models of planar last passage percolation, it is known that geodesics of length $n$ exhibit transversal fluctuations at scale $n^{2/3}$ and matching (up to exponents) upper and lower bounds for the tail probabilities…
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…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
The term "moderate deviations" is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak…
We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space $D(0,\infty)$.…
Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…
We present and analyze a momentum-based gradient method for training linear classifiers with an exponentially-tailed loss (e.g., the exponential or logistic loss), which maximizes the classification margin on separable data at a rate of…
We study the problem of bounding path-dependent expectations (within any finite time horizon $d$) over the class of discrete-time martingales whose marginal distributions lie within a prescribed tolerance of a given collection of benchmark…