Speaker:  Milind Hegde (University of Columbia) 

Title: The lower tail of q-pushTASEP

Abstract: The Kardar-Parisi-Zhang class is a broad class of models which are believed to exhibit universal behaviors. Currently, detailed information is known essentially only for a handful of models with algebraic connections, known as integrable models. In the past decade, however, some progress has been made in studying some non-integrable settings, where a crucial input has been quantitative bounds on upper and lower tails of the relevant observable in related integrable settings. Of the two, the lower tail is typically more challenging. In the context of "zero-temperature" models, a number of tools are available for this tail, but the situation is not as developed in positive temperature. We will discuss q-pushTASEP, an integrable interacting particle system and a positive temperature model, for which nevertheless a connection to the zero-temperature model of last passage percolation was recently discovered by Imamura-Mucciconi-Sasamoto. We use this to develop a new method to obtain bounds on the lower tail for the location of the right-most particle under step initial data.

Joint work with Ivan Corwin.