Abstract:
Over the last five years substantial progress has been made in understanding how random interlacements disconnect macroscopic bodies. In this talk we discuss a result pertaining to the strongly percolative regime of the vacant set, and the occurrence of an excessive fraction of sites in a large box that gets disconnected by the interlacements from the boundary of a concentric box of double size. If, as expected, the critical levels for percolation and strong percolation of the vacant set coincide, this result expresses the principal exponential rate of decay of the probability of this large deviation event in terms of a variational problem in the continuum, which involves the percolation function for the vacant set of random interlacements.
Biography:
Alain-Sol Sznitman has been at ETH Zurich since 1991 when he was appointed Full Professor in the Department of Mathematics. He was director of the FIM (Mathematics Research Institute) from 1995 until 1999.
Alain-Sol Sznitman was born in 1955 in Paris. He studied at the École Normale Supérieure in Paris. Following his studies he became Attaché de Recherche at CNRS in 1979, and worked at the Laboratoire de Probabilités de l'Université Pierre et Marie Curie. In 1983 he received the Doctorat d’État, became Chargé de Recherche and spent two years at the Courant Institute in New York, returning to Paris in 1985. In 1987 he was appointed Associate Professor at the Courant Institute and in 1990 Full Professor. In 1989 Alain-Sol Sznitman received the Alfred P. Sloan Fellowship, and in 1991 the Rollo Davidson Prize. In 1992 he presented a Plenary Lecture at the First European Congress of Mathematics in Paris. In 1998 he was an Invited Speaker at the International Congress of Mathematicians in Berlin, and in 1999 he received the Line and Michèle Loève Prize. In 2008 he became Member of the Academia Europaea, in 2012 member of the Inaugural Class of AMS Fellows, and in 2014 member of the IMU Circle.
Alain-Sol Sznitman’s research concerns probability theory, with a special focus on problems connected with physics, in particular problems of random media. He is the author of several scientific publications and member of several scientific committees.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai