These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …

We consider the minimum of a super-critical branching random walk. Addario-Berry and
Reed [Ann. Probab. 37 (2009) 1044–1079] proved the tightness of the minimum centered …

In this article, we investigate the extremal values of (the logarithm of) the characteristic
polynomial of a random unitary matrix whose spectrum is distributed according to the …

In the present paper, we show that under the Riemann hypothesis, and for fixed h, ϵ> 0 h,
ϵ> 0, the supremum of the real and the imaginary parts of\log ζ (1/2+ it) log ζ (1/2+ it) for t ∈ …

We consider the boundary case (in the sense of Biggins and Kyprianou Electron. J. Probab.
10 (2005) 609–631 in a one-dimensional super-critical branching random walk, and study …

Consider a critical branching random walk on the real line. In a recent paper, Aïdékon
(2011) developed a powerful method to obtain the convergence in law of its minimum after a …

Nous étudions le maximum d'un champ Gaussien sur [0, 1] d (d≥ 1) dont les corrélations
décroissent logarithmiquement avec la distance. Kahane (Ann. Sci. Math. Québec 9 (1985) …

There has been tremendous progress recently in the understanding of the extreme value
statistics of stochastic processes whose variables exhibit strong correlations. The purpose of …

Consider a branching random walk evolving in a macroscopic time-inhomogeneous
environment, that scales with the length n of the process under study. We compute the first …

We consider a catalytic branching random walk on Z that branches at the origin only. In the
supercritical regime we establish a law of large number for the maximal position Mn: For …