Abstract:
In a joint work with Izumi Okada, we study the capacity of the range of a simple random walk in three and higher dimensions. It is known that the order of the capacity of the random walk range in k dimensions has a similar asymptotic to that of the volume of the random walk range in k-2 dimensions.
Proving the law of the iterated logarithm for the capacity of the range, we find that this correspondence breaks down for k=3, leading to an unexpected host of challenging open problems.
Biography:
Professor Amir Dembo is a mathematician known for his work in probability theory. He received all his degrees in Electrical Engineering from the Technion - Israel Institute of Technology, obtaining a DSc in 1986 (with David Malah as adviser). After post docs at Brown University Applied Mathematics and at Stanford's Electrical Engineering, he joined Stanford university as Assistant Professor of Statistics and Mathematics in 1990. He is currently the Marjorie Mhoon Fair Professor of Quantitative Science and Professor of Mathematics and Statistics in the School of Humanities and Sciences at Stanford University.
Professor Dembo’s research focuses on probability theory and stochastic processes, information theory, and large deviations theory. His work has applications in communications, control systems, and biomolecular sequence analysis. He spoke at the International Congress of Mathematicians in Madrid, and is a fellow of the IMS. He was elected a member of the National Academy of Sciences in 2022 and of the American Academy of Arts and Sciences in 2023.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.