Abstract:
In this talk we present large deviation lower bounds for the probability of certain bulk-deviation events depending on the occupation-time field of a simple random walk on the Euclidean lattice in dimensions larger or equal to three. As a particular application, these bounds imply an exact leading order decay rate for the probability of the event that a simple random walk covers a substantial fraction of a macroscopic body, when combined with a corresponding upper bound previously obtained by Sznitman. As a pivotal tool for deriving such optimal lower bounds, we recall the model of tilted walks which was first introduced by Li in order to develop similar large deviation lower bounds for the probability of disconnecting a macroscopic body from an enclosing box by the trace of a simple random walk. We then discuss a refined local coupling with the model of random interlacements which is used to locally approximate the occupation times of the tilted walk.
Based on joint work with A. Chiarini (University of Padova).
Biography:
Maximilian Nitzschner is currently an Assistant Professor at the Hong Kong University of Science and Technology (HKUST). He obtained his B. Sc. and M. Sc. in Physics in 2014 and 2016, respectively, as well as his B. Sc. and M. Sc. in Mathematics in 2015 and 2016, respectively, at the University of Heidelberg. In 2020, he completed his Dr. Sc. in Mathematics under the supervision of Prof. Dr. Alain-Sol Sznitman at ETH Zurich. Following his doctoral studies, he held a postdoctoral position as Courant Instructor at the Courant Institute of Mathematical Sciences at New York University between 2020 and 2023 and joined HKUST in August 2023. His research is primarily in probability theory and mathematical physics, with a focus on disordered media, percolation, and random walks.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.