Ideas Seminar: Erik Bates, NCSU

Title: The Busemann process for (1+1)-dimensional directed polymers

Abstract: Busemann functions have been decidedly instrumental in advancing our understanding of first-passage percolation and last-passage percolation, both in general and exactly solvable cases.   The Busemann theory has been less developed, however, for their positive-temperature counterparts: directed polymers.  This talk will highlight some recent progress on that front, namely in understanding the Busemann process simultaneously across all directions in the plane.  We will see some reassuring similarities with the zero-temperature setting, but also some intriguing differences. The exactly solvable inverse-gamma model will be our star witness.  Joint work with Wai-Tong (Louis) Fan and Timo Seppäläinen.