相关论文: Sums of projections with random coefficients
Let $M$ be a semifinite von Neumann algebra and $T$ a positive contraction on both $L^1(M)$ and $L^\infty(M)$. We consider ergodic averages along a random sparse subsequence determined by independent Bernoulli variables $(X_n)_{n\geq 1}$…
We investigate spectral properties of a discrete random displacement model, a Schr\"odinger operator on $\ell^2(\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of…
The extension of the concept of $p-$summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space $M$…
We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the…
Given a pure state vector |x> and a density matrix rho, the function p(x|rho)=<x|rho|x> defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to…
We extend the Wiener-Khinchin theorem to non-wide sense stationary (WSS) random processes, i.e. we prove that, under certain assumptions, the power spectral density (PSD) of any random process is equal to the Fourier transform of the…
The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…
In this paper the notion of an EPR state for the composite S of two quantum systems S1, S2, relative to S2 and a set O of bounded observables of S2, is introduced in the spirit of classical examples of Einstein-Podolsky-Rosen and Bohm. We…
By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
The method of Alternating Projections (AP) is a fundamental iterative technique with applications to problems in machine learning, optimization and signal processing. Examples include the Gauss-Seidel algorithm which is used to solve…
Let $H_0$ and $H$ be a pair of self-adjoint operators satisfying some standard assumptions of scattering theory. It is known from previous work that if $\lambda$ belongs to the absolutely continuous spectrum of $H_0$ and $H$, then the…
We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…
We introduce a random matrix model where the entries are dependent across both rows and columns. More precisely, we investigate matrices of the form $\X=(X_{(i-1)n+t})_{it}\in\R^{p\times n}$ derived from a linear process $X_t=\sum_j c_j…
We introduce different ensembles of random Lindblad operators $\cal L$, which satisfy quantum detailed balance condition with respect to the given stationary state $\sigma$ of size $N$, and investigate their spectral properties. Such…
We revisit the concept of spectral averaging and point out its origin in connection with one-parameter subgroups of $SL_2(\bbR)$ and the corresponding M\"obius transformations. In particular, we identify exponential Herglotz representations…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
The famous results of Koml\'os, Major and Tusn\'ady (see [15] and [17]) state that it is possible to approximate almost surely the partial sums of size n of i.i.d. centered random variables in L p (p > 2) by a Wiener process with an error…
We study expectation values of matrix elements for boundary values of the resolvent as well as the density of states for a random Schr\"odinger operator with potential distributed according to a Poisson process. Asymptotic expansions for…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…