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.