Some Applications of Variational Techniques in Stochastic Geometry I

Explore applications of variational techniques in stochastic geometry in this 47-minute lecture by Giovanni Peccati. Delve into basic tools of stochastic analysis on the Poisson space and learn how they can be applied to develop variational inequalities for assessing the magnitude of variances of geometric quantities. Focus on Poincaré, L1/L2, OSSS, and Schramm-Steif inequalities, as well as their connections to noise sensitivity and superconcentration. Examine the Boolean model, Gilbert graph, and examples of random variables. Investigate Maldivian calculus, operators, and vineyard chaoses. Based on joint works with I. Nourdin, X. Yang, Yogeshwaran D., and G. Last, this talk provides insights into variance estimates on the Poisson space.

Introduction
Outline
Definition
Boolean model
Gilbert graph
Examples of random variables
Maldivian calculus
Operators
Vineyard chaoses