Probability and Statistics Seminar: Central moments of the free energy of the O'Connell-Yor polymer

Friday, September 25, 2020 at 3:30pm to 4:30pm

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Philippe Sosoe, Cornell University

We estimate the central moments of the stationary semi-discrete polymer in a Brownian environment, also known as the O’Connell-Yor polymer.   From  previous  work  of  Seppalainen  and  Valko,  it  is known that for certain choices of the parameters, the variance growth this governed by the exponent 2/3, characteristic of fluctuations of models in the KPZ class.
We develop formulas based on Gaussian integration by parts to relate higher cumulants of the free energy to expectations of products of quenched  cumulants  of  the  first  jump from  the  boundary  into  the system.   We  then  use  these  formulas  to  obtain  estimates  for  all central moments and the moments of the first jump (corresponding to the transversal fluctuations). The bounds are of nearly optimal order $1/3 + \epsilon$, resp. $2/3+\epsilon$, with $\epsilon$ arbitrary.
I will also discuss an extension of this work to certain discrete polymers in random environment.
Joint work with Christian Noack.

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