# Difference between revisions of "Probability Seminar"

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== February 4, 2021, [https://cims.nyu.edu/~hbchen/ Hong-Bin Chen] (Courant Institute, NYU) == | == February 4, 2021, [https://cims.nyu.edu/~hbchen/ Hong-Bin Chen] (Courant Institute, NYU) == | ||

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+ | '''Dynamic polymers: invariant measures and ordering by noise''' | ||

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+ | We develop a dynamical approach to infinite volume polymer measures (IVPM) in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow, and establish ordering by noise. We prove that, for a fixed asymptotic slope, the polymer dynamics has a unique invariant distribution given by a unique IVPM. Moreover, One Force-One Solution principle holds. | ||

== February 11, 2021, [https://mathematics.stanford.edu/people/kevin-yang Kevin Yang] (Stanford) == | == February 11, 2021, [https://mathematics.stanford.edu/people/kevin-yang Kevin Yang] (Stanford) == |

## Revision as of 17:17, 30 January 2021

# 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

If you would like to sign up for the email list to receive seminar announcements then please join our group.

## January 28, 2021, no seminar

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

**Dynamic polymers: invariant measures and ordering by noise**

We develop a dynamical approach to infinite volume polymer measures (IVPM) in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow, and establish ordering by noise. We prove that, for a fixed asymptotic slope, the polymer dynamics has a unique invariant distribution given by a unique IVPM. Moreover, One Force-One Solution principle holds.

## 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.