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 …

This volume introduces readers to the world of disordered systems and to some of the
remarkable probabilistic techniques developed in the field. The author explores in depth a …

We study the asymptotic behavior of a multidimensional random walk in a general cone. We
find the tail asymptotics for the exit time and prove integral and local limit theorems for a …

Abstract Let denote a Haar Unitary matrix of dimension and consider the field for. Then, in
probability. This provides a verification up to second order of a conjecture of Fyodorov …

Abstract Let S 0= 0, S n, n≥ 1 be a random walk generated by a sequence of iid random
variables X 1, X 2,... and let τ^-=\rm min {n ≧ 1: S_ n ≦ 0\} and τ^+=\rm min {n\geq1: S_ n> …

Let {Sn} be a random walk in the domain of attraction of a stable law Y, ie there exists a
sequence of positive real numbers (an) such that Sn/an converges in law to Y. Our main …

Let η^*_n denote the maximum, at time n, of a nonlattice one-dimensional branching
random walk n possessing (enough) exponential moments. In a seminal paper, Aïdekon …

We prove an invariance principle for the bridge of a random walk conditioned to stay
positive, when the random walk is in the domain of attraction of a stable law, both in the …

Abstract Let (X_n) _ n\geqslant 0 (X n) n⩾ 0 be a Markov chain with values in a finite state
space XX starting at X_0= x ∈ XX 0= x∈ X and let f be a real function defined on X X. Set …