Moments of partition functions of 2D Gaussian polymers in the weak disorder regime

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• Ofer Zeitouni (Weizmann Institute of Science)
• Friday 12 July 2024, 14:00-15:00
• Seminar Room 1, Newton Institute.

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SSDW01 - Self-interacting processes

We consider the directed two dimensional polymer in Gaussian iid environment, using the subcritical scaling $\beta\sim c/\sqrt{\log n}$. In this scaling, the partition function has logarithmically decaying correlations, with a rather peculiar covariance profile. Motivated by the study of the field of partition functions indexed by their startng point, we compute the leading order of high (order of $\sqrt{\log N}$) moments, exhibiting this covariance profile, and explain how these can be used in order to discuss extremes of the field. Joint work with Clement Cosco (Paris), and part of work in progress with him and Shuta Nakajima (Tokyo). 

This talk is part of the Isaac Newton Institute Seminar Series series.

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