# Probability Seminar

# Spring 2021

**Thursdays in 901 Van Vleck Hall at 2:30 PM**, unless otherwise noted.
**We usually end for questions at 3:20 PM.**

** IMPORTANT: ** In Spring 2021 the seminar is being run online. ZOOM LINK

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## January 28, 2021, no seminar

## February 4, 2021, Hong-Bin Chen (Courant Institute, NYU)

## February 11, 2021, Kevin Yang (Stanford)

## February 18, 2021, Ilya Chevyrev (Edinburgh)

## February 25, 2021, Roger Van Peski (MIT)

## March 4, 2021, Roland Bauerschmidt (Cambridge)

## March 11, 2021, Sevak Mkrtchyan (Rochester)

**The limit shape of the Leaky Abelian Sandpile Model**

The leaky abelian sandpile model (Leaky-ASM) is a growth model in which n grains of sand start at the origin in the square lattice and diffuse according to a toppling rule. A site can topple if its amount of sand is above a threshold. In each topple a site sends some sand to each neighbor and leaks a portion 1-1/d of its sand. This is a dissipative generalization of the Abelian Sandpile Model, which corresponds to the case d=1.

We will discuss how, by connecting the model to a certain killed random walk on the square lattice, for any fixed d>1, an explicit limit shape can be computed for the region visited by the sandpile when it stabilizes.

We will also discuss the limit shape in the regime when the dissipation parameter d converges to 1 as n grows, as this is related to the ordinary ASM with a modified initial configuration.