We consider the set of points visited by the random walk on the discrete torus $(\mathbb
{Z}/N\mathbb {Z})^ d $, for $ d\geq 3$, at times of order $ uN^ d $, for a parameter $ u> 0$ in …

In this paper we establish a decoupling feature of the random interlacement process Iu⊂ Zd
at level u, d≥ 3. Roughly speaking, we show that observations of Iu restricted to two disjoint …

We study the percolative properties of random interlacements on G× ℤ, where G is a
weighted graph satisfying certain sub-Gaussian estimates attached to the parameters α> 1 …

We consider a simple random walk on a discrete torus\input amssym (\BbbZ/N\BbbZ)^d with
dimension d≥ 3 and large side length N. For a fixed constant u≥ 0, we study the percolative …

In this book, we discuss stochastic processes on random graphs. The understanding of such
processes is interesting from an applied perspective, since random graphs serve as models …

We study the level-set of the zero-average Gaussian Free Field on a uniform random d-
regular graph above an arbitrary level h∈(−∞, h⋆), where h⋆ is the level-set percolation …

We consider continuous time interlacements on ℂ d, d≥ 3, and investigate the scaling limit
of their occupation times. In a suitable regime, referred to as the constant intensity regime …

We provide an explicit algorithm for sampling a uniform simple connected random graph
with a given degree sequence. By products of this central result include:(1) continuum …

In this article we obtain for d≥ 3 an approximation of the zero-average Gaussian free field
on the discrete d-dimensional torus of large side length N by the Gaussian free field on Z d …

We review and comment recent research on random interlacements model introduced by A.-
S. Sznitman in the paperVacant set of random interlacements and percolation'(Ann. of Math …