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Lecture notes of a master course given at Orsay between 2019-2024. Topics covered include Part I: One-dimensional random walks, cycle lemma and Bienaym\'e--Galton--Watson random trees. Part II: Erd\"os--R\'enyi random graphs, three proofs…

Randomized algorithms have propelled advances in artificial intelligence and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science,…

This is a report of a scientific project carried out at Ecole Centrale Casablanca in 2019. This work is an entry into the world of Random Walk in a Random Environment (RWRE). We will discuss some intuitive concepts such as recurrence,…

We survey several results known on sampling in computational geometry.

Lecture Notes. Minicourse given at the workshop "Activated Random Walks, DLA, and related topics" at IM\'eRA-Marseille, March 2015.

Recent progress on the understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the…

This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].

First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…

This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.

This article gives a brief survey of the theory and applications of anomalies.

We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.

The following random process on $\Z^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk…

A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…

This article summarizes recent trends in mobile biometrics.

This paper is a short review on the application of continuos-time random walks to Econophysics in the last five years.

This note contains old instead of new results about random walks on groups, which may serve as a small supplement to the author's monograph ``Random Walks on Infinite Graphs and Groups'' (Cambridge Univ. Press 2000/2009). First, we exhibit…

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions.

In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.

This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of…

. In this paper we give a survey of some recent results for random walk in random scenery (RWRS). On $\mathbb {Z}^d$, $d\geq 1$, we are given a random walk with i.i.d. increments and a random scenery with i.i.d. components. The walk and the…