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