Mathematical and Theoretical Physics Seminar (MTPS)

Abbas Saberi (MPIPKS Dresden, University of Tehran)

Emergence at the Edge: Random Matrices Meet Correlated Percolation

Abstract: Random matrix theory and percolation are two foundational frameworks based on ensembles of independent random variables. Despite their deceptively simple formulations, both exhibit rich and nontrivial behavior, leading to widespread applications in describing diverse physical phenomena and advancing interdisciplinary research. In this talk, I will begin with a general overview of these two theories and highlight some of their real-world applications---including the modeling of economic systems, large-scale climate wind variables, and electrical and thermal conduction in polymer nanocomposites. We will then examine the limitations of these classical models in the presence of long-range correlations, which are common in natural systems. Drawing on ideas from correlated percolation, I will show how one can construct a new class of random matrix ensembles that incorporate long-range correlations and uncover novel spectral universality classes. I will conclude with examples demonstrating how these concepts apply to long-range correlated quantum and classical systems.

Athanasios Chatzistavrakidis (RBI Zagreb)

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Christiaan J.F. van de Ven (FAU Erlangen-Nürnberg)

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