Marston Morse Lectures

(This lecture will be self-contained.) In high dimensions, what does it look like when we take the intersection of a set of random half-spaces with either the sphere or the Hamming cube? This is one phrasing of the so-called perceptron problem...

(This lecture is related to the preceding lecture, but I will try to make it self-contained as much as possible.) In this lecture I will elaborate on some of the existing mathematical approaches to the study of random CSPs, particularly involving...

I will describe recent progress in determination of asymptotic behavior in random constraint satisfaction problems, including the independent set problem on random graphs, random regular NAE-SAT, and random SAT. The results include sharp phase...

Fluctuations look like white noise

Laure Saint-Raymond
At leading order, the fluctuations around the typical dynamics are described by the second cumulant. They actually satisfy a stochastic PDE with time-space white noise. Can we say more using higher order cumulants?

Space-time correlations at equilibrium

Laure Saint-Raymond
Although the distribution of hard spheres remains essentially chaotic in this regime, collisions give birth to small correlations. The structure of these dynamical correlations is amazing, going through all scales. How combinatorial techniques...

Disorder increases almost surely.

Laure Saint-Raymond
Consider a system of small hard spheres, which are initially (almost) independent and identically distributed. Then, in the low density limit, their empirical measure $\frac1N \sum_{i=1}^N \delta_{x_i(t), v_i(t)}$ converges almost surely to a...