Related papers: REM universality for linear random energy
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
Let X be a compact complex manifold endowed with a big line bundle L. We define the energy at equilibrium of a weighted subset as the Monge-Ampere energy of the associated extremal plurisubharmonic weight. We prove the differentiability of…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
Lepton universality, meaning the equal coupling of the electroweak gauge bosons to the different lepton flavours, is a central property of the Standard Model (SM). Tests of lepton universality in ratios of rates of $b\to s\ell^+\ell^-$…
We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max…
The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient and meta-gradient density functionals. The results are compared with the…
In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, transition energy field…
We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…
Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. This was proven in a large class of models…
We study invariant random matrix ensembles \begin{equation*} \mathbb{P}_n(d M)=Z_n^{-1}\exp(-n\,tr(V(M)))\,d M \end{equation*} defined on complex Hermitian matrices $M$ of size $n\times n$, where $V$ is real analytic such that the…
It is shown that excitation spectra of Generalized Gibbs Ensembles (GGE) of one-dimensional integrable models with isotopic symmetry contain universal features insensitive to details of the distribution. Namely, the low energy limit of the…
We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap…
The expressions for the energy-weighted sum rule of the isoscalar and isovector coordinate operators are derived based on the second-order fluctuation of the local densities. Conventional derivation of the Thouless theorem for the…
We study the probability density function $P(h_m,L)$ of the maximum relative height $h_m$ in a wide class of one-dimensional solid-on-solid models of finite size $L$. For all these lattice models, in the large $L$ limit, a central limit…
We consider the local eigenvalue distribution of large self-adjoint $N\times N$ random matrices $\mathbf{H}=\mathbf{H}^*$ with centered independent entries. In contrast to previous works the matrix of variances $s_{ij} = \mathbb{E}\,…
A statistical system is classically defined on a set of microstates $E$ by a global energy function $H : E \to \mathbb{R}$, yielding Gibbs probability measures (softmins) $\rho^\beta(H)$ for every inverse temperature $\beta = T^{-1}$. Gibbs…
We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…
A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian systems. The universality appears in middle energy regime and is different from another universality which can be reproduced by random matrices in the following two…
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…