My research area is probability theory. Most of my research has been in random walks in random environments (RWRE), but I am also interested in other non-classical random walks (such as excitedâ€¦ (More)

We consider a nearest-neighbor, one dimensional random walk {Xn}nâ‰¥0 in a random i.i.d. environment, in the regime where the walk is transient but with zero speed, so that Xn is of order n for some sâ€¦ (More)

i Acknowledgments First of all, I would like to thank God. I dare not, in pride, pretend that any accomplishment I have achieved is of my own doing. My life has been blessed in so many ways by thingsâ€¦ (More)

We derive properties of the rate function in Varadhanâ€™s (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zeroâ€¦ (More)

We consider a nearest-neighbor, one-dimensional random walk {Xn}nâ‰¥0 in a random i.i.d. environment, in the regime where the walk is transient with speed vP > 0 and there exists an s âˆˆ (1, 2) suchâ€¦ (More)

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter Îº > 0 thatâ€¦ (More)

We study the contact process on the complete graph on n vertices where the rate at which the infection travels along the edge connecting vertices i and j is equal to Î»wiwj/n for some Î» > 0, where wiâ€¦ (More)

This lecture notes arose out of a mini-course I taught in January 2013 at Instituto Nacional de MatemÃ¡tica pura e Aplicada (IMPA) in Rio de Janeiro, Brazil. In these lecture notes I do not alwaysâ€¦ (More)

We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions forâ€¦ (More)

We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed vP . We give upper boundsâ€¦ (More)