Dear all, you are kindly invited to attend the seminar given in Padova by Prof. G. Giacomin. Here are the details:
* Date: 30 October 2023
* Room: 2AB40, Torre Archimede
* Title: Products of random matrices and the statistical mechanics of disordered Ising chains
* Abstract: A general issue in statistical mechanics is understanding the role of disorder: disordered models are models that are made more realistic by allowing the presence of impurities. We consider this question in the basic context of Ising spin chains with nearest neighbor interaction J and random external field (the disorder). The matrix transfer method allows to rewrite the model in terms of a product of random matrices: in particular, the free energy density coincides with the top Lyapunov exponent. I will explain why the limit of J tending to infinity is of particular interest. As a matter of fact, for this limit one finds in the physical literature a remarkable prediction based on a renormalization group approach (work of Daniel Fisher in the 90s). We (collaboration with Orphée Collin and Yueyun Hu) have recently proven this prediction in the case in which the external field is centered. I will explain the result and some ideas from the proof by highlighting the interplay that arises in this problem between the theory of random matrix products and stochastic analysis.
The seminar will *only* be in presence. See you there, thanks, The Padova Probability Group