#### Room 217

#### Webinar: Combinatorics of an exclusion process driven by an asymmetric tracer

#### Arvind Ayyer

##### IISc, Bangalore

*To be held via Zoom. Meeting ID: 87273633652.*

We consider an exclusion process on a periodic one-dimensional lattice where all particles perform simple symmetric exclusion except for a _tracer particle_, which performs partially asymmetric exclusion with forward and backward rates p and q respectively. This process and its variants have been investigated starting with Ferrari, Goldstein and Lebowitz (1985) motivated by questions in statistical physics. We prove product formulas for stationary weights and exact formulas for the nonequilibrium partition function in terms of combinatorics of set partitions. We will also compute the current, and the density profile as seen by the test particle. Time permitting, we will illustrate the ideas involved in performing asymptotic analysis. This talk is based on the preprint arXiv:2001.02425.

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