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8 papers · 2 filters
From fermionic spin-Calogero-Sutherland models to the Haldane-Shastry chain by freezing
Jules Lamers, Didina Serban
The Haldane-Shastry spin chain has a myriad of remarkable properties, including Yangian symmetry and, for spin , explicit highest-weight eigenvectors featuring (the case $α= 1…
Bernoulli variables, classical exclusion processes and free probability
Michel Bauer, Denis Bernard, Philippe Biane +1
We present a new description of the known large deviation function of the classical symmetric simple exclusion process by exploiting its connection with the quantum symmetric simpl…
Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
Thomas Chouteau, Sofia Tarricone
Solutions of the discrete Painlevé II hierarchy are shown to be in relation with a family of Toeplitz determinants describing certain quantities in multicritical random partitions…
Exponents for Hamiltonian paths on random bicubic maps and KPZ
Philippe Di Francesco, Bertrand Duplantier, Olivier Golinelli +1
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exac…
Rigorous dynamical mean field theory for stochastic gradient descent methods
Cedric Gerbelot, Emanuele Troiani, Francesca Mignacco +2
We prove closed-form equations for the exact high-dimensional asymptotics of a family of first order gradient-based methods, learning an estimator (e.g. M-estimator, shallow neural…
Spaces of states of the two-dimensional O(n) and Potts models
Jesper Lykke Jacobsen, Sylvain Ribault, Hubert Saleur
We determine the spaces of states of the two-dimensional and -state Potts models with generic parameters as representations of their known symmetry al…