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Lectures on Coulomb and Riesz gases
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This is the preliminary version of a book on Coulomb and Riesz gases that grew out of a set of notes written for graduate courses taught at the Courant Institute, at the Ecole Normale Sup\'erieure, and at the 2024 Saint-Flour Probability summer school.
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Cited by 10 Pith papers
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Sharp mean-field estimates for the repulsive log gas in any dimension
The log-gas partition function is uniformly bounded in N for arbitrary bounded base measures, giving a mean-field convergence rate of order 1/N instead of (log N)/N for repulsive logarithmic interactions.
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Fluctuations of two-dimensional determinantal processes associated with Berezin--Toeplitz operators
For free-fermion determinantal processes associated with Berezin-Toeplitz operators, smooth linear statistics satisfy a two-term Szegő-type expansion and a Gaussian CLT with variance equal to half the H1 seminorm in t...
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Nonlinear Stability and Instability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with General Pressure Laws
Steady states of attractive compressible Euler-Riesz flows are unstable in the mass-supercritical polytropic range and orbitally stable as energy minimizers in the subcritical/general-pressure regime, with relative-en...
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An indefinite Coulomb interaction from the Steklov spectrum of perforated manifolds
Steklov eigenvalues of a manifold with many small critically-sized holes converge to weighted Laplace–Beltrami eigenvalues at the optimal rate, with the next-order term given by an indefinite Coulomb energy mediated b...
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Wasserstein gradient flows for Coulomb discrepancies
Wasserstein gradient flows of Coulomb MMD exist globally, become instantly bounded, decay exponentially on the torus via a defective PL inequality, but face spatial-infinity obstructions on R^d.
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McKean-Vlasov SDEs with Local Distributional Interactions: Well-Posedness and Entropy-Cost Estimates
McKean-Vlasov SDEs with distributional local negative-Sobolev kernels have global well-posedness from smoothed initial laws and entropy-cost estimates.
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Equilibrium measures for higher dimensional rotationally symmetric Riesz gases
Given a radially symmetric equilibrium density, the paper reconstructs the external potential generating it, verifies the Euler-Lagrange conditions, and applies the method to power-law densities, power-law potentials,...
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Free-energy variations for determinantal 2D plasmas with holes
For a determinantal 2D Coulomb gas with small well-separated holes, the correlation energy is independent of hole locations up to O(1), and adding holes changes it by explicit topological log N terms.
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Poisson Statistics for Coulomb Gases at Intermediate Temperature Regimes
For 2D Coulomb gases with temperature beta between 1/N and 1/(sqrt(N) log N), the microscopic point process converges to a homogeneous Poisson point process with intensity equal to the equilibrium measure density.
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Partition function of 2D Coulomb gases with radially symmetric potentials and a hard wall
For radially symmetric potentials at beta = 2, the log N coefficient in the hard-wall partition function is -1/4 for an annulus and -1/3 for a disk when the wall lies strictly inside the droplet, instead of the usual -1/12.
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