Subhajit Goswami
TIFR, Mumbai
August 31, 2023
Sharp threshold phenomena and the geometry of large random sets: Phase transition commonly refers to the abrupt change of behavior in a physical system when one or more parameters (e.g., temperature) are changed continuously. Rigorous understanding of this ubiquitous phenomenon has been one of the main drivers in the development of mathematical physics and probability theory since the latter half of twentieth century. In this talk, we will review some of the key notions in this area and highlight their connections with ergodic theory, functional analysis and random fractals among others. Most of the corresponding results are classically known for random systems where the underlying probability measure resembles a product measure in a certain sense and this is often a very serious limitation for answering many natural questions arising from other areas of probability theory and random geometry. We will outline some recent conceptual progress that we made in this regard towards the end of the talk.
TIFR, Mumbai
August 31, 2023
Sharp threshold phenomena and the geometry of large random sets: Phase transition commonly refers to the abrupt change of behavior in a physical system when one or more parameters (e.g., temperature) are changed continuously. Rigorous understanding of this ubiquitous phenomenon has been one of the main drivers in the development of mathematical physics and probability theory since the latter half of twentieth century. In this talk, we will review some of the key notions in this area and highlight their connections with ergodic theory, functional analysis and random fractals among others. Most of the corresponding results are classically known for random systems where the underlying probability measure resembles a product measure in a certain sense and this is often a very serious limitation for answering many natural questions arising from other areas of probability theory and random geometry. We will outline some recent conceptual progress that we made in this regard towards the end of the talk.