##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability Seminar

## Dr. Izumi Okada

#### Kyushu University

## Capacity of the range of random walk

##### Abstract:

We study the capacity of the range of a simple random walk in three and higher dimensions. It is known that the order of the capacity of the random walk range in n dimensions is similar to that of the volume of the random walk range in n-2 dimensions. We show that this correspondence breaks down for the law of the iterated logarithm for the capacity of the random walk range in three dimensions. We also prove the law of the iterated logarithm in higher dimensions.

This is joint work with Amir Dembo.

### November 17, 2022

### 11:00 AM

Room 6402 with live streaming.

Zoom ID: 947 1948 3503.

Email poagarwal@ucsd.edu for password

Research Areas

Probability Theory****************************