Related papers: Some Theory for the Analysis of Random Fields - Wi…

This PhD thesis is organized as follows. In the first two chapters I will review some basic notions of statistical physics of disordered systems, such as random graph theory, the mean-field approximation, spin glasses and combinatorial…

This is the author's PhD thesis, which focuses on the so-called Landau-Ginzburg/conformal field theory correspondence. This correspondence dates from the late 80s and early 90s in the physics literature and in particular, it predicts a…

Motivated by the papers of Mladenovc and Piterbarg (2006), Krajka (2011) and Pereira and Tan (2017), we study the limit properties for the maxima from nonstationary random fields subject to missing observations and obtain the weakly…

This is my Ph.D. thesis written under the direction of Prof. Joseph Bernstein at Tel-Aviv University. Submitted: March 2005.

The article is a lightly edited version of my habilitation thesis at the University Wuerzburg. My aim is to give a self contained, if concise, introduction to the formal methods used when off-line learning in feedforward networks is…

This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.

This review is an extended version of my mini course at the Etats de la recherche: Operateurs de Schroedinger aleatoires at the Universite Paris 13 in June 2002, a summer school organized by Frederic Klopp. These lecture notes try to give…

The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…

This PhD thesis focuses on local conformal nets of von Neumann algebras on the circle. For a more detailed description of its content and of the results published within, see its preface.

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

This Ph.D. thesis collects results obtained investigating two different aspects of modern unifying theories. In the first part I summarized results achieved investigating simplicial aspects of string dualities. Exploiting Boundary Conformal…

In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…

This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…

This thesis presents a new methodology to analyze one-dimensional signals trough a new approach called Multi Layer Analysis, for short MLA. It also provides some new insights on the relationship between one-dimensional signals processed by…

A discussion of the method of multiscale analysis in the study of localization of random operators based on lectures given at \emph{Random Schr\"odinger operators: methods, results, and perspectives}, \'Etats de la recherche, Universit\'e…

This Bachelor's thesis, written in Russian, is devoted to a relatively new direction in the field of machine learning and artificial intelligence, namely probabilistic programming. The thesis gives a brief overview to the already existing…

This habilitation thesis is cumulative and, therefore, is collecting and connecting research that I (together with several co-authors) have conducted over the last few years. Thus, the absolute core of the work is formed by the ten…

Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…

We review recent developments on the characterization of random landscapes in high-dimension. We focus in particular on the problem of characterizing the landscape topology and geometry, discussing techniques to count and classify its…

These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…