Home /   Pinning of directed polymers and the Baik-Ben Arous-Péché phase transition

Seminar

Pinning of directed polymers and the Baik-Ben Arous-Péché phase transition August 30, 2021 (11:00 AM PDT - 12:00 PM PDT)
Parent Program:
Location: SLMath: Online/Virtual, Eisenbud Auditorium
Speaker(s) Guillaume Barraquand (Centre National de la Recherche Scientifique (CNRS))
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Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
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Video

Pinning Of Directed Polymers And The Baik-Ben Arous-Péché Phase Transition
Abstract/Media

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Models of directed polymers confined by a wall are expected to obey a phase transition as the strength of the noise along the wall increases. This was first predicted in 1985 in physics by Kardar. We will show that for an exactly sovable model, the log-gamma polymer, the partition function of polymers confined to an octant of the Z^2 lattice with free endpoint indeed satisfies a phase transition. Near the critical point, the statistics are asymptotically distributed as in the Baik-Ben Arous-Péché phase transition for outliers of Hermitian random matrices. The talk is based on a recent preprint joint with Shouda Wang, and will also touch on earlier works with Alexei Borodin and Ivan Corwin, with Ivan Corwin and Evgeni Dimitrov, and with Pierre Le Doussal.

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Pinning Of Directed Polymers And The Baik-Ben Arous-Péché Phase Transition