CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by ...

Random fields and Gaussian processes constitute fundamental frameworks in modern probability theory and spatial statistics, providing robust tools for modelling complex dependencies over space and ...

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric ...

In the first part of the course, we will start with an introduction to the Gaussian free field (GFF), which is an object which has been at the heart of some recent groundbreaking developments in ...

Random analytic functions are a fundamental object of study in modern complex analysis and probability theory. These functions, often defined through power series with random coefficients, exhibit ...