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Numerical study of the inverse-gamma 1+1 directed polymer

Walschaerts, Sébastien
(2024)

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Details

Supervisors
Claeys, Tom ; Ruelle, Philippe
Faculty
Faculté des sciences
Degree label
Master [120] en sciences physiques, à finalité approfondie
Abstract
This thesis is a numerical study of the 1+1 dimensional directed polymer model in an inverse-gamma distributed random environment. This model with only one spatial dimension is a fundamental and well-studied case in the theory of directed polymers. The choice of an inverse-gamma distribution provides strong analytical foundations and acts as an essential example within the KPZ universality class. The numerical results reveal that the free energy fluctuations converge to the Tracy-Widom distribution, in agreement with theoretical predictions for systems in the KPZ universality class. This study takes inspiration from three known theorems, which are verified. This work provides deeper insights into the inverse-gamma 1+1 directed polymer model, for which the implications extend to several fields and applications where understanding the interplay between disorder and growth phenomena is essential.