## Theoretical Statistics and Mathematics Division

### Indian Statistical Institute, Kolkata.

203 Barrackpore Trunk Road, Kolkata 700108, India

## Ashok Maitra Memorial Lectures 2019-20

### Professor Leonid Mytnik

Faculty of Industrial Engineering and Management
TECHNION, Israel Institute of Technology
Web: https://web.iem.technion.ac.il/en/people/userprofile/leonidm.html

will deliver the Ashok Maitra Memorial Lectures 2019-20 at

Video recordings of some of the lectures can be found here :

### At Indian Statistical Institute, Delhi Centre

#### Abstract:

We study the asymptotic speed of a random front for solutions to stochastic reaction-diffusion equations with multiplicative noise proportional to $\sigma$. We show existence of the speed of the front and derive its asymptotics as $\sigma$ goes to infinity. This also gives us information on the speed of propagation of the branching-coalescent system of Brownian motions with high rate of coalescence.

This is a joint work with C. Mueller and L. Ryzhik.

### At Indian Statistical Institute, Kolkata

#### Abstract:

We study the boundary of $d$-dimensional super-Brownian motion in dimensions $d\leq 3$. Super-Brownian motion is the measure-valued process that arises as a scaling limit of critical branching Brownian motions. It is well-known that in dimension $d=1$ the density of the super-Brownian is given by the unique in law solution of the SPDE \begin{eqnarray} \nonumber \frac{\partial X}{\partial t}= \frac12 \Delta X + \sqrt{X}\dot{W} \end{eqnarray} where $\dot{W}$ is the Gaussian space-time white noise. In dimension $d=1$, the Hausdorff dimension of the boundary of the zero set of $X_t$ is established for fixed times $t>0$. In dimensions $d\leq 3$ the boundary of the range of the super-Brownian motion is studied, and as a consequence we also establish results on the boundary of the Brownian motion indexed by the continuous random tree (CRT).

The talk is based on joint works with C.Mueller, E.Perkins and J. Hong.

### At Indian Statistical Institute, Bangalore Centre

#### Abstract:

We study regularity properties and the boundary of $d$-dimensional super-Brownian motion in dimensions $d\leq 3$. Super-Brownian motion is the measure-valued process that arises as a scaling limit of critical branching Brownian motions. It is well-known that in dimension $d=1$ the density of the super-Brownian is given by the unique in law solution of the SPDE \begin{eqnarray} \nonumber \frac{\partial X}{\partial t}= \frac12 \Delta X + \sqrt{X}\dot{W} \end{eqnarray} where $\dot{W}$ is the Gaussian space-time white noise. We discuss the regularity properties of the density of the super-Brownian motion. In particular, the Hausdorff dimension of the boundary of the zero set of the density $X_t$ is established for fixed times $t>0$. In dimensions $d\leq 3$ the boundary of the range of the super-Brownian motion is studied, and as a consequence we also establish results on the boundary of the Brownian motion indexed by the continuous random tree (CRT).

The talk is based on joint works with C.Mueller, E.Perkins and J. Hong.

Theoretical Statistics and Mathematics Unit
Head Quarters and Other Centres