Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in
which the problem was reduced to the study of certain" random surfaces". He further made …

We consider the dimer model on the square and hexagonal lattices with doubly periodic
weights. Although in the near-critical regime the Kasteleyn matrix is related to a massive …

In this note we show that the 2D continuum Gaussian free field (GFF) admits an excursion
decomposition that is on the one hand similar to the classical excursion decomposition of …

We develop an approach for investigating geometric properties of Gaussian multiplicative
chaos (GMC) in an infinite dimensional set up. The base space is chosen to be the space of …

This thesis concentrates on the classical problem of understanding the multifractal
properties of Brownian motion and random walk. Specifically, we will be interested in the set …

Quadratic harnesses are Markov polynomial processes with linear conditional expectations
and quadratic conditional variances with respect to past-future filtrations. Typically, they are …