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   Busto-Moner, Luis; Feng, Chi-Jui; Antoszewski, Adam; Tokmakoff, Andrei; Dinner, Aaron R. (October 2021, Biochemistry)
2. Adding flavor to the Narain ensemble

   https://doi.org/10.1007/JHEP05(2022)090  

   Datta, Shouvik; Duary, Sarthak; Kraus, Per; Maity, Pronobesh; Maloney, Alexander (May 2022, Journal of High Energy Physics)

   A bstract We revisit the proposal that the ensemble average over free boson CFTs in two dimensions — parameterized by Narain’s moduli space — is dual to an exotic theory of gravity in three dimensions dubbed U(1) gravity. We consider flavored partition functions, where the usual genus g partition function is weighted by Wilson lines coupled to the conserved U(1) currents of these theories. These flavored partition functions obey a heat equation which relates deformations of the Riemann surface moduli to those of the chemical potentials which measure these U(1) charges. This allows us to derive a Siegel-Weil formula which computes the average of these flavored partition functions. The result takes the form of a “sum over geometries”, albeit with modifications relative to the unflavored case. 

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3. The Binary Expansion Randomized Ensemble Test

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   Lee, Duyeol; Zhang, Kai; Kosorok, Michael R. (January 2024, Statistica Sinica)
4. Operator limit of the circular beta ensemble

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5. Generalized Gibbs Ensemble of the Ablowitz–Ladik Lattice, Circular $$\beta $$-Ensemble and Double Confluent Heun Equation

   https://doi.org/10.1007/s00220-023-04642-8  

   Grava, Tamara; Mazzuca, Guido (May 2023, Communications in Mathematical Physics)

   Abstract We consider the discrete defocusing nonlinear Schrödinger equation in its integrable version, which is called defocusing Ablowitz–Ladik lattice. We consider periodic boundary conditions with period N and initial data sampled according to the Generalized Gibbs ensemble. In this setting, the Lax matrix of the Ablowitz–Ladik lattice is a random CMV-periodic matrix and it is related to the Killip-Nenciu Circular $$\beta $$ β -ensemble at high-temperature. We obtain the generalized free energy of the Ablowitz–Ladik lattice and the density of states of the random Lax matrix by establishing a mapping to the one-dimensional log-gas. For the Gibbs measure related to the Hamiltonian of the Ablowitz–Ladik flow, we obtain the density of states via a particular solution of the double-confluent Heun equation. 

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