Student Probability

Title: The hierarchical model

Abstract: We cover Chapter 4 of "Introduction to a Renormalisation Group Method". Motivated by the finite-range decomposition of Euclidean GFFs, we introduce the hierarchical GFF (hGFF) model. After discussing its construction and properties, we also define…

Title: Intro to the renormalization group method

 Abstract: In this talk, I will introduce a class of problems that have inspired the use of the renormalization group method. I will discuss spin models and the regimes for which renormalization is relevant, and some aspects of Gaussian…

We continue to discuss Talagrand's book on generic chaining.

We will discuss a method to bound covering numbers as one often hopes to do in chaining, specifically in the context of empirical counting processes. Symmetrization and the use of VC dimension are included.

We will discuss how the majorizing measure theorem can be applied to hypergraph sparsification.

We continue to study Talagrand's book, "Upper and Lower Bounds for Stochastic Processes". In particular, we start Chapter 3.

We continue studying Talagrand's book, "Upper and Lower Bounds for Stochastic Processes". In particular, we will cover Chapter 3.

Continuing from previous talks, we discuss the remaining sections of Chapter 2 in Talagrand's book. First, we construct a sequence of partitions that satisfy a certain quantitative inequality (Theorem 2.9.1). Using this result, we prove the majorizing measure theorem (Theorem 2.10.1), which…

Abstract

Abstract