Tracy-Widom asymptotics for a random polymer model with\n gamma-distributed weights
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Abstract
We establish Tracy-Widom asymptotics for the partition function of a random\npolymer model with gamma-distributed weights recently introduced by\nSepp\\"al\\"ainen. We show that the partition function of this random polymer can\nbe represented within the framework of the geometric RSK correspondence and\nconsequently its law can be expressed in terms of Whittaker functions. This\nleads to a representation of the law of the partition function which is\namenable to asymptotic analysis. In this model, the partition function plays a\nrole analogous to the smallest eigenvalue in the Laguerre unitary ensemble of\nrandom matrix theory.\n
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