Related papers: Time-frequency concentration of generating systems
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
A uniformly bounded complete orthonormal system of functions $\Theta =\{ \theta_n\}_{n=1}^{\infty},$ $ \|\theta_n\|_{L^\infty_{[0,1]} } \leq M $ is constructed such that $\sum_{n=1}^{\infty} a_{n}\theta_{n}$ converges almost everywhere on…
The quantum fluctuations of the entropy production for fermionic systems in the Landauer-Buttiker non-equilibrium steady state are investigated. The probability distribution, governing these fluctuations, is explicitly derived by means of…
The formation of patterns in driven systems has been studied extensively, and their emergence can be connected to a fine balance of instabilities and stabilization mechanisms. While the early phase of pattern formation can be understood on…
We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…
We experimentally investigate the steady states of two granular assemblies differing in their material properties and allowed to exchange volume with each other under external agitation in the vicinity of their jamming transition. We…
There has recently been a concerted effort to derive mechanisms in vision and machine learning systems to offer uncertainty estimates of the predictions they make. Clearly, there are enormous benefits to a system that is not only accurate…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…
We study an information-theoretic measure of uncertainty for quantum systems. It is the Shannon information $I$ of the phase space probability distribution $\la z | \rho | z \ra $, where $|z \ra $ are coherent states, and $\rho$ is the…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
Fluctuation-response relations encode fundamental constraints on nonequilibrium systems. While time-domain static response is bounded by activity and entropy production, finite-frequency extensions for time-dependent perturbations remain…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
We prove that the local eigenvalue statistics for $d=1$ random band matrices with fixed bandwidth and, for example, Gaussian entries, is given by a Poisson point process and we identify the intensity of the process. The proof relies on an…
An approach to the problem of 1/f voltage noise observed in all conducting media is developed based on an uncertainty relation for the Fourier-transformed signal. It is shown that the quantum indeterminacy caused by non-commutativity of…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
The author establishes a new mathematical expression for the Frequency Polygon. He uses it to prove the strong uniform consistency of the Frequency Polygon marginal density estimator for non-anticipative stationary stochastic processes…
We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms…