相关论文: Local Laws and a Mesoscopic CLT for $\beta$-ensemb…
The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…
Coarse-grain Lagrangian methods, such as Dissipative Particle Dynamics ( Hoogerbrugge et al., EPL, 1992), are suitable for describing mesoscopic fluid systems that include thermal fluctuations. However, the realistic simulation of liquids…
We obtain a CLT for $\log|\det(M_n-s_n)|$ where $M_n$ is a scaled Laguerre $\beta$ ensemble and $s_n=d_++\sigma_n n^{-2/3}$ with $d_+$ denoting the upper edge of the limiting spectrum of $M_n$ and $\sigma_n$ a slowly growing function…
We study the Central Limit Theorem (CLT) in the so-called hybrid Lebesgue-continuous spaces and tail behavior of normed sums of centered random independent variables (vectors) with values in these spaces.
We introduce a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms. We deal with merely L 1 initial data, general self-adjoint pure jump L{\'e}vy operators, and locally Lipschitz nonlinearities of…
We show that the classical (mean-field) description of far from equilibrium superconductivity is exact in the thermodynamic limit for local observables but breaks down for global quantities, such as the entanglement entropy or Loschmidt…
This paper is about nonequilibrium steady states (NESS) of a class of stochastic models in which particles exchange energy with their "local environments" rather than directly with one another. The physical domain of the system can be a…
Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point…
The local entropy of a nonequilibrium system of independent fermions is investigated, and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of…
The central limit theorem for convex bodies says that with high probability the marginal of an isotropic log-concave distribution along a random direction is close to a Gaussian, with the quantitative difference determined asymptotically by…
We define a notion of logarithmic, Coulomb and Riesz interactions in any dimension for random systems of infinite charged point configurations with a uniform background of opposite sign. We connect this interaction energy with the…
The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density $n$, leading…
A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, a law of large numbers is shown to hold in a…
Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…
The coordinate Bethe Ansatz solution of the log-gamma polymer is extended to boundary conditions with one fixed end and the other attached to one half of a one-dimensional lattice. The large-time limit is studied using a saddle-point…
We study the energy deposition in a one dimensional interacting quantum system with a point like potential modulated in amplitude. The point like potential at position $x=0$ has a constant part and a small oscillation in time with a…
We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…
In this paper we propose a new approach to the central limit theorem (CLT), based on functions of bounded F\'echet variation for the continuously differentiable linear statistics of random matrix ensembles which relies on: a weaker form of…
This paper proves that a wide class of local search algorithms extend as is to the fully dynamic setting with an adaptive adversary, achieving an amortized $\tilde{O}(1)$ number of local-search steps per update. A breakthrough by Moser…