To participate in this seminar, please register HERE.

We provide an introduction to recent results on the large N behavior of beta-ensembles, also known as log-gases. In the first part, we focus on the rigidity property of the spectrum which provides fine estimates on the fluctuations of eigenvalues and explain how this relate to universality. In the second part, we explain how to prove the CLT for linear statistics using loop equations and mention the connection to log-correlated fields and Gaussian multiplicative chaos.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To participate in this seminar, please register HERE.

In this course I will present two techniques to construct Fredholm determinants starting from an integrable system. One of these techniques will be based on the Riemann-Hilbert method and the other only requires the knowledge of the associated linear system. My choice of examples will be Painlev\'e equations, although the techniques are applicable to a wide variety of problems.

To participate in this seminar, please register HERE.

For uniformly random permutations of length n, it is well known that the length of the longest increasing subsequence is very close to 2 \sqrt{n}. More generally, the Schensted shape of the permutation (under Schensted insertion) rescaled by 1/\sqrt{n} converges to a certain non-random limit shape and described by Vershik--Kerov and Logan--Shepp. When looking at a sequence of numbers which claims to be "pseudo-random", one could ask whether the longest increasing subsequence and the Schensted shape have similar limits. For most pseudo-random sequences, I do not know the answer to this question so there will be some open questions posed. For the sequence consisting of the fractional parts of multiples of an irrational number, the answer is "no", and I will discuss joint work with T. Kyle Petersen which explores the behavior of the Schensted shape, which can be described explicitly in terms arithmetic properties of the irrational number which generates the sequence.

To participate in this seminar, please register HERE.

To participate in this seminar, please register HERE.

The stochastic block model has been one of the most fruitful research topics in community detection and clustering. We consider the community detection problem in a sparse random tensor model called the hypergraph stochastic block model. Angelini et al. (2015) conjectured a threshold for detecting the community structure in this model, and we confirmed the positive part of the phase transition in the 2-block case. We introduced a matrix that counts self-avoiding walks on random hypergraphs, whose leading eigenvectors give a correlated reconstruction of the community. Based on joint work with Soumik Pal.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To participate in this seminar, please register HERE.

To participate in this seminar, please register HERE.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To participate in this seminar, please register HERE.

We prove an exact limit shape of the KPZ equations under weak noise scaling, when we condition the value of the KPZ equations at one point to be very large. We also show that under such conditioning, the shape of the noise in the KPZ equation is asymptotically given by the optimizer of the L^4 Gagliardo-Nirenberg-Sobolev inequality.

To participate in this seminar, please register HERE.

We consider the simple exclusion process on $\Z\times\{0,1\}$, that is,  an ``horizontal  ladder'' composed of $2$ lanes. Particles can jump according to a lane-dependent translation-invariant nearest neighbour jump kernel, i.e. ``horizontally'' along each lane, and ``vertically'' along the scales of the ladder. We analyze the set of extremal invariant measures for this model. (Joint work with Gidi Amir, Christophe Bahadoran and Ofer Busani. ArXiv : 2105.12974

To participate in this seminar, please register HERE.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.

To register for this course, go to: https://www.msri.org/seminars/26228

This class aims at understanding some important classes of smooth random functions of very many variables.

What can be said about the complexity of the topology of the landscapes they define?

How efficient are the natural exploration or optimization algorithms in these landscapes?

The toolbox of Random Matrix Theory will be used for both questions.

We will concentrate on two wide classes of interesting smooth random functions of many variables.

A first source of such functions is to be found in statistical mechanics of disordered systems, i.e. the Hamiltonians of disordered models, like spin-glasses. There the randomness is assumed to model quenched disorder in the medium.

Another rich class of such functions comes from Data Science and studies the random landscapes of inference problems in high-dimensional statistical estimation. Here the randomness of these landscapes is the randomness inherent in sampling.