Related papers: Extrema of log-correlated random variables: Princi…

We review recent progress relating to the extreme value statistics of the characteristic polynomials of random matrices associated with the classical compact groups, and of the Riemann zeta-function and other $L$-functions, in the context…

We study a branching random walk with independent and identically distributed, heavy tailed displacements. The offspring law is supercritical and satisfies the Kesten-Stigum condition. We treat the case when the law of the displacements…

A recent conjecture of Fyodorov--Hiary--Keating states that the maximum of the absolute value of the Riemann zeta function on a typical bounded interval of the critical line is $\exp\{\log \log T -\frac{3}{4}\log \log \log T+O(1)\}$, for an…

This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed…

These lecture notes offer a gentle introduction to the two-dimensional Discrete Gaussian Free Field with particular attention paid to the scaling limits of the level sets at heights proportional to the absolute maximum. The bulk of the text…

We study the behavior of the Riemann zeta function on the critical line when the imaginary part of the argument is sampled by the Cauchy random walk. We develop a complete second order theory for the corresponding system of random variables…

We consider point process convergence for sequences of iid random walks. The objective is to derive asymptotic theory for the largest extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the…

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…

We show that the centered maximum of a sequence of log-correlated Gaussian fields in any dimension converges in distribution, under the assumption that the covariances of the fields converge in a suitable sense. We identify the limit as a…

This article extends the results of Fang & Zeitouni (2012a) on branching random walks (BRWs) with Gaussian increments in time inhomogeneous environments. We treat the case where the variance of the increments changes a finite number of…

We continue the study of the maximum of the scale-inhomogeneous discrete Gaussian free field in dimension two. In this paper, we consider the regime of weak correlations and prove the convergence in law of the centred maximum to a randomly…

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

In this paper, we study a random field constructed from the two-dimensional Gaussian free field (GFF) by modifying the variance along the scales in the neighborhood of each point. The construction can be seen as a local martingale transform…

We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length $(\log T)^{\theta}$, where $\theta$ is either fixed or tends to zero at a suitable rate. It is shown that the deterministic…

We revisit the statistics of extremes and records of symmetric random walks with stochastic resetting, extending earlier studies in several directions. We put forward a diffusive scaling regime (symmetric step length distribution with…

We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…

This work extends the studies on the minimum and extremal process of a supercritical branching random walk outside the boundary case which cannot be reduced to the boundary case. We study here the situation where the log-generating function…

In recent work, Fyodorov and Keating conjectured the maximum size of $|\zeta(1/2+it)|$ in a typical interval of length O(1) on the critical line. They did this by modelling the zeta function by the characteristic polynomial of a random…

This paper is a complement to the studies on the minimum of a real-valued branching random walk. In the boundary case (Biggins, Kyprianou 2005), A\"{i}d\'ekon in a seminal paper (2013) obtained the convergence in law of the minimum after a…

This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…