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arXiv · 2212.05649

Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2\,$ spin dynamics for Wigner and Wishart ensembles

Vincent Lahoche·Dine Ousmane Samary·Mohamed Tamaazousti
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Abstract

In this paper, we investigate the large-time behavior for a slightly modified version of the standard p=2 soft spins dynamics model, including a quartic or higher potential. The equilibrium states of such a model correspond to an effective field theory, which has been recently considered as a novel paradigm for signal detection in data science based on the renormalization group argument. We consider a Langevin-like equation, including a disorder term that leaves in the Wigner or Wishart ensemble. Then we construct a nonperturbative renormalization group formalism valid in the large N limit, where eigenvalues distributions for the disorder can be replaced by their analytic limits, namely the Wigner and Marchenko-Pastur laws. One of the main advantages of this approach is that the interactions remain local in time, avoiding the non-locality arising from the approaches that integrate out the disorder at the partition function level.

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Vincent Lahoche, Dine Ousmane Samary, Mohamed Tamaazousti. 2022-12-12. Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2\,$ spin dynamics for Wigner and Wishart ensembles. https://doi.org/10.1088/2399-6528%2Facd09d

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