Thomas Mountford

D'origine britannique, né en 1961. Il a reçu la bourse présidentielle des jeunes investisseurs (Presidential Young Investigator Grant) en 1990 et le prix de la Fraternité Sloan (Sloan Fellowship) en 1991. Son travail montre que les valeurs critiques d'une classe large de de systèmes de particules proches sont égales à 1, et que, suite à plusieurs travaux sur la trajectoire du mouvement brownien, incluant une simulation numérique, le nombre d'îlots browniens en 2 dimensions tend vers l'infini quand leurs tailles tendent vers 0. Il reçoit le prix Rosenbaum en 1993 lui ouvrant ainsi les portes du Isaac Newton Institute à Cambridge. Il est également décoré par le prix Rollo Davidson en 1995 et nommé membre honoraire de l'Institute of Mathematical Statistics en 2001.

Assistant Profeseur de Mathematique a UCLA 1987- 1991

Associate Professeur de Mathematique a UCLA 1991-1993

Professeur de Mathematique a UCLA 1993-2001

Professeur Departement de mathématiques, EPFL dès 2001

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MATH-101(en): Analysis I (English)

We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable.

MATH-432: Probability theory

The course is based on Durrett's text book Probability: Theory and Examples.
It takes the measure theory approach to probability theory, wherein expectations are simply abstract integrals.

MATH-332: Stochastic processes

The course follows the text of Norris and the polycopie (which will be distributed chapter by chapter).

In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs.

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n2. The function f(n) is said to be "asymptotically equivalent to n2, as n → ∞". This is often written symbolically as f (n) ~ n2, which is read as "f(n) is asymptotic to n2".

We consider one-dimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the sta

2021

Flooding And Diameter In General Weighted Random Graphs

Thomas Mountford, Jacques Saliba

In this paper we study first passage percolation on a random graph model, the configuration model. We first introduce the notions of weighted diameter, which is the maximum of the weighted lengths of

CAMBRIDGE UNIV PRESS2020

On the probability distribution of the local times of diagonally operator-self-similar Gaussian fields with stationary increments

Thomas Mountford, Kamran Kalbasi

In this paper, we study the local times of vector-valued Gaussian fields that are 'diagonally operator-selfsimilar' and whose increments are stationary. Denoting the local time of such a Gaussian fiel

INT STATISTICAL INST2020