Related papers: REM universality for linear random energy
The energy distribution in the most general nonstatic spherically symmetric space-time is obtained using M{\o}ller's energy-momentum complex. This result is compared with the energy expression obtained by using the energy-momentum complex…
We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of…
The energy-momentum distribution of spatially homogeneous rotating spacetimes in the context of teleparallel theory of gravity is investigated. For this purpose, we use the teleparallel version of Moller prescription. It is found that the…
Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation…
We find new estimates and a new asymptotic decoupling phenomenon for solutions to Hitchin's self-duality equations at high energy. These generalize previous results for generically regular semisimple Higgs bundles to arbitrary Higgs…
Let $X$ be an $n\times n$ matrix with independent and identically distributed entries $x_{ij} \stackrel{\text { d }}{=} n^{-1 / 2} x$ for some complex random variable $x$ of mean zero and variance one. Let $\{\sigma_i\}_{1\le i\le n}$ be…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically given by a generalization of the Gaudin-Mehta distribution,…
Let $\{\Lambda_n=\{\lambda_{1,n},\ldots,\lambda_{d_n,n}\}\}_n$ be a sequence of finite multisets of real numbers such that $d_n\to\infty$ as $n\to\infty$, and let $f:\Omega\subset\mathbb R^d\to\mathbb R$ be a Lebesgue measurable function…
We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic…
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…
We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…
We consider the non-Hermitian analogue of the celebrated Wigner-Dyson-Mehta bulk universality phenomenon, i.e. that in the bulk the local eigenvalue statistics of a large random matrix with independent, identically distributed centred…
We analyze the eigenvalues of the adjacency matrices of a wide variety of random trees. Using general, broadly applicable arguments based on the interlacing inequalities for the eigenvalues of a principal submatrix of a Hermitian matrix and…
The Hamiltonian approach to the General Relativity and the Standard Model is studied in the context of its consistency with the Newton law, the Higgs effect, the Hubble cosmological evolution and the Cosmic Microwave Background radiation…
For a quantum system in a macroscopically large volume $V$, prepared in a pure state and subject to maximally noisy or ergodic unitary dynamics, the reduced density matrix of any sub-system $v\ll V$ is almost surely totally mixed. We show…
Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…
We study statistical properties of energy spectra of a tight-binding model on the two-dimensional quasiperiodic Ammann-Beenker tiling. Taking into account the symmetries of finite approximants, we find that the underlying universal…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…