Related papers: Asymptotic Distribution of Eigenvalues for a Self-…

In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.

In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…

Asymptotic properties of the local Whittle estimator in the nonstationary case (d>{1/2}) are explored. For {1/2}<d\leq 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of…

Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…

We provide formulas for the entropy of free-string states depending on their mass, charges and size, both in bosonic and superstring theory (IIA or IIB). We properly define these quantities in full-fledged string theory. We then investigate…

The amplitude of localized quantum states in random or disordered media may exhibit long range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these…

The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…

The damping of the axionic string motion due to the surrounding plasma is estimated by a detailed calculation of the fermion scatter from a global string and it is shown that the friction force on the string can be neglected before the…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

We consider a disordered one-dimensional tight-binding model with power-law decaying hopping amplitudes to disclose wavefunction maximum distributions related to the Anderson localization phenomenon. Deeply in the regime of extended states,…

We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the…

We calculate the density of states with given mass and spin in string theory and obtain asymptotic formulas. We also compute the tree-level gyromagnetic couplings for arbitrary physical states in the heterotic string theory. These results…

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…

A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…

We investigate the asymptotic distribution of the profile likelihood ratio (PLR) when constraining effective field theories (EFTs) and show that Wilks' theorem is often violated, meaning that we should not assume the PLR to follow a…

We study the distribution of eigenvalues for non-selfadjoint perturbations of selfadjoint semiclassical analytic pseudodifferential operators in dimension two, assuming that the classical flow of the unperturbed part is completely…

The density of states of self-gravitational system diverges when the particles are spread to infinity. Other problem based an inhomogeneous distribution of particles,which motivate the gravitational interaction. In this sense the…

We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…

The arbitrary functions principle says that the fractional part of $nX$ converges stably to an independent random variable uniformly distributed on the unit interval, as soon as the random variable $X$ possesses a density or a…