On the Lyapunov exponent of random transfer matrices and on pinning models with constraints

Abstract : This work is made of two independent parts. - The first is devoted to the study of the Lyapunov exponent of a product of random transfer matrices. This Lyapunov exponent appears repeatedly in the statistical mechanics literature, notably in the analysis of the Ising model in some special disordered environments. The focus is on a singular behaviour that has been pointed out in the physical literature: we provide a mathematical analysis of this singularity. - In the second part we consider a variation of the Poland-Scheraga model for DNA denaturation. This variation aims at modeling the case of circular DNA. We provide a complete analysis of the homogeneous model, including free energy regularity and critical behaviour, as well as path properties. We also tackle the disordered case, for which we prove relevance of disorder both for the free energy and the trajectories of the system.
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Submitted on : Thursday, February 13, 2020 - 4:58:20 PM
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Benjamin Havret. On the Lyapunov exponent of random transfer matrices and on pinning models with constraints. Mathematical Physics [math-ph]. Université de Paris, 2019. English. ⟨tel-02478078⟩



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