English
Related papers

Related papers: On the gap between deterministic and probabilistic…

200 papers

We study the spectral norm of random lifts of matrices. Given an $n\times n$ symmetric matrix $A$, and a centered distribution $\pi$ on $k\times k\ (k\ge 2)$ symmetric matrices with spectral norm at most $1$, let the matrix random lift…

Probability · Mathematics 2021-06-03 Afonso S. Bandeira , Yunzi Ding

Let $G$ be a locally compact group and $\mu$ a probability measure on $G,$ which is not assumed to be absolutely continuous with respect to Haar measure. Given a unitary representation $(\pi, \cal H)$ of $G,$ we study spectral properties of…

Dynamical Systems · Mathematics 2015-02-04 Bachir Bekka , Yves Guivarc'h

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…

Probability · Mathematics 2012-05-31 Olga Friesen , Matthias Löwe

We analyze theoretically and experimentally how nonlinear differential-transmission spectroscopy of a lambda-system medium can provide quantitative understanding of the optical dipole moments and transition energies. We focus on the…

Materials Science · Physics 2015-01-07 J. P. de Jong , A. R. Onur , D. Reuter , A. D. Wieck , C. H. van der Wal

Let the map $f:[-1,1]\to[-1,1]$ have a.c.i.m. $\rho$ (absolutely continuous $f$-invariant measure with respect to Lebesgue). Let $\delta\rho$ be the change of $\rho$ corresponding to a perturbation $X=\delta f\circ f^{-1}$ of $f$. Formally…

Dynamical Systems · Mathematics 2009-11-10 David Ruelle

This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…

Optimization and Control · Mathematics 2010-09-08 Debasish Chatterjee , Daniel Liberzon

We study discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics. These models are widely studied in event history analysis, and are characterized by the state space, the initial distribution and…

To better understand the surprising low-frequency vibrational modes in structural glasses, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network…

Disordered Systems and Neural Networks · Physics 2018-10-31 E M Stanifer , P K Morse , A A Middleton , M L Manning

Girko matrices have independent and identically distributed entries of mean zero and unit variance. In this note, we consider the random matrix model formed by the ratio of two independent Girko matrices, its entries are dependent and…

Probability · Mathematics 2026-03-19 Djalil Chafaï , David García-Zelada , Yuan Yuan Xu

We investigate the thermodynamic limit of Dicke superradiance. We find an expression for the system's density matrix that we can prove is exact in the limit of large atom numbers N. This is in contrast to previously known solutions whose…

Quantum Physics · Physics 2022-07-26 Daniel Malz , Rahul Trivedi , Ignacio Cirac

Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…

Machine Learning · Statistics 2015-07-24 Robert Mattila , Cristian R. Rojas , Bo Wahlberg

The mixed radio frequency (RF)/free-space optical (FSO) relaying is a promising technology for coverage improvement, while there lacks unified expressions to describe its performance. In this paper, a unified performance analysis framework…

Information Theory · Computer Science 2015-07-22 Jiayi Zhang , Linglong Dai , Yu Zhang , Zhaocheng Wang

This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…

Probability · Mathematics 2019-05-02 Adrian N. Bishop , Pierre Del Moral

Let $G$ be a graph with adjacency matrix $A(G)$ and let $D(G)$ be the diagonal matrix of the degrees of $G$. For any real $\alpha\in [0,1]$, Nikiforov [Merging the $A$- and $Q$-spectral theories, Appl. Anal. Discrete Math. 11 (2017)…

Combinatorics · Mathematics 2018-05-16 Huiqiu Lin , Xing Huang , Jie Xue

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…

Disordered Systems and Neural Networks · Physics 2009-10-31 M. Mezard , G. Parisi , A. Zee

Let A be an n x n symmetric random matrix whose upper-triangular entries are independent and follow possibly non-identical subgaussian distributions. This paper investigates the spectral properties of A, including its eigenvalues and…

Probability · Mathematics 2026-04-14 Zeyan Song , Hanchao Wang

We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential…

Probability · Mathematics 2010-11-01 Sourav Chatterjee , Persi Diaconis , Allan Sly

We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…

Functional Analysis · Mathematics 2007-05-23 I. V. Krasovsky

We establish a sharp lower bound on the spectral gap of the biased adjacent-transposition Markov chain on the symmetric group. As a consequence, we resolve a longstanding conjecture of Fill, proving that among all regular probability…

Probability · Mathematics 2026-04-08 Gary R. W. Greaves , Haoran Zhu

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…

Adaptation and Self-Organizing Systems · Physics 2014-04-14 Ankit Kumar , Vidit Agrawal , Sudeshna Sinha