### 25/04/2022

Adrian Redder, 2:30PM

*Age of information in time-varying networks under strongly mixing communication **(slides)*

Sayantan Maitra, 2:45PM

*Weak uniqueness of stochastic heat equation **(slides)*

Sarath Yasodharan, 3:00PM

*A sufficient condition for the quasipotential to be the rate function of the invariant measure of the countable-state mean-field interacting particle system **(slides)*

Tran Hoang Son, 3:30PM

*Quantitative Marcinkiewicz's theorem and central limit theorems: applications to spin systems and point processes **(slides)*

Ujan Gangopadhyay, 3:45PM

*Transverse increments in two-dimensional first passage percolation **(slides)*

### 02/05/2022

Priyanka Sen, 2:30PM

*Random matrices with independent entries: beyond non-crossing partitions **(slides)*

Anugu Sumith Reddy, 2:45PM

*Selecting Feller weak solution in degenerate diffusions **(slides)*

Sayan Mukherjee, 3:00PM

*Regularized Bayesian best response learning in finite games **(slides)*

Sibsankar Singha, 3:15PM

*Characterization of multivariate risk measures **(slides)*

## Bangalore Probability Seminar

### Some of the old BPS talks:

(Click here for past BPS seminars and the BPS calendar)

2022/01/24

Title: The geometry of random spherical eigen functions

Abstract: A lot of efforts have been devoted in the last decade to the investigation of the high-frequency behaviour of geometric functionals for the excursion sets of random spherical harmonics, i.e., Gaussian eigenfunctions for the spherical Laplacian. In this talk we shall review some of these results, with particular reference to the asymptotic behaviour of variances, phase transitions in the nodal case (the Berry’s Cancellation Phenomenon), the distribution of the fluctuations around the expected values, and the asymptotic correlation among different functionals. We shall also discuss some connections with the Gaussian Kinematic Formula, with Wiener-Chaos expansions and with recent developments in the derivation of Quantitative Central Limit Theorems (the so-called Stein-Malliavin approach).

Title: Nodal length of random eigen functions: a detailed overview

Abstract: We thoroughly investigate the behavior of the nodal length of high-frequency random eigenfunctions, starting from the spherical case. As anticipated by the previous talk, the powerful combination of chaotic techniques and reduction principles allows to prove a Central Limit Theorem for random spherical harmonics, which holds for shrinking domains as well. For Gaussian Laplace eigenfunctions on the torus instead, the number-theoretical nature of the problem leads to non-Gaussian second order fluctuations, also observed all the way down to Planck scale. As for 'generic' Riemannian surfaces, the case of the whole manifold is still an open problem, however there are results at small scales that take advantage of Berry's scaling limit and some new coupling techniques.