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SUMMARY:Fluctuation bounds for O'Connell-Yor type systems - Philippe Sosoe
  (Cornell)
DTSTART:20210309T140000Z
DTEND:20210309T150000Z
UID:TALK158020@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:The O'Connell-Yor polymer is a fundamental model of a polymer 
 in a\nrandom environment. It corresponds to the positive temperature versi
 on\nof Brownian Last Passage percolation. Although much is known about thi
 s model thanks to remarkable algebraic structure uncovered by O'Connell\, 
 Yor and others\, basic estimates for the behavior of the tails of the cent
 ered partition function for finite N that are available for zero temperatu
 re models are missing. I will present an iterative estimate to obtain stro
 ng concentration and localization bounds  for the O'Connell-Yor polymer on
  an almost optimal scale N^{1/3+\\epsilon}. \n\nIn the second part of the 
 talk\, I will introduce a system of interacting diffusions describing the 
 successive increments of partition functions of different sizes. For this 
 system\, the N^{2/3} variance upper bound known for the OY polymer can be 
 proved for a general class of interactions which are not expected to corre
 spond to integrable models.\n\nJoint work with Christian Noack and Benjami
 n Landon.
LOCATION:Zoom
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