Related papers: Limit theorems for the evolution of quantum pure s…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…
We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case…
We give a central limit theorem, which has applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced generalized Polya urns.
Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels,…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of probability distributions is described. The sufficient condition…
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
An application of Levy's continuity theorem and Hankel transform allow us to establish a law limit theorem for the sequence $V_n=f(U)\sin(n U)$, where $U$ is uniformly distributed in $(0,1)$ and $f$ a given function. Further, we investigate…
In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.
Upper and lower bounds are established for the survival probability $|<\psi(0)|\psi(t)>|^{2}$ of a quantum state, in terms of the energy moments $<\psi(0)|H^{n}|\psi(0)>$. Introducing a cut-off in the energy generally enables considerable…
For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$,…
Entropic arguments are shown to play a central role in the foundations of quantum theory. We prove that probabilities are given by the modulus squared of wave functions, and that the time evolution of states is linear and also unitary.
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for…
A general law is presented for (composite) quantum systems which directly describes the time evolution of quantum states (with one or both components) through an arbitrary noisy quantum channel. It is shown that the time evolution of all…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
The deleting items theorems of weak law of large numbers (WLLN),strong law of large numbers (SLLN) and central limit theorem (CLT) are derived by substituting partial sum of random variable sequence with deleting items partial sum. We…
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…