Spectral gap for an unrestricted Kawasaki type dynamics
Spectral gap for an unrestricted Kawasaki type dynamics
We give an accurate asymptotic estimate for the gap of the generator of a particular interacting particle system. The model we consider may be informally described as follows. A certain number of charged particles moves on the segment [1,L] according to a Markovian law. One unitary charge, positive or negative, jumps from a site k to another site k'=k+1 or k'=k-1 at a rate which depends on the charge at site k and at site k'. The total charge of the system is preserved by the dynamics, in...
Spectral gap for the interchange process in a box.
Spectral gap lower bound for the one-dimensional fractional Schrödinger operator in the interval
We prove a uniform lower bound for the difference λ₂ - λ₁ between the first two eigenvalues of the fractional Schrödinger operator , α ∈ (1,2), with a symmetric single-well potential V in a bounded interval (a,b), which is related to the Feynman-Kac semigroup of the symmetric α-stable process killed upon leaving (a,b). “Uniform” means that the positive constant appearing in our estimate is independent of the potential V. In the general case of α ∈ (0,2), we also find a uniform lower bound for...
Spectral gaps and exponential integrability of hitting times for linear diffusions
Let X be a regular continuous positively recurrent Markov process with state space ℝ, scale function S and speed measure m. For a∈ℝ denote Ba+=supx≥am(]x, +∞[)(S(x)−S(a)), Ba−=supx≤am(]−∞; x[)(S(a)−S(x)). It is well known that the finiteness of Ba± is equivalent to the existence of spectral gaps of generators associated with X. We show how these quantities appear independently in the study of the exponential moments of hitting times of X. Then we establish a very direct relation between exponential...
Spectral Multiplicity of Certain Gaussian Processes
Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices.
Spectral properties of large random matrices with independent entries
We consider large Wigner random matrices and related ensembles of real symmetric and Hermitian random matrices. Our results are related to the local spectral properties of these ensembles.
Spectral representation of isotropic random currents
Spectral statistics for random Schrödinger operators in the localized regime
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy in the localized phase. Assume the density of states function is not too flat near . Restrict it to some large cube . Consider now , a small energy interval centered at that asymptotically contains infintely many eigenvalues when the volume of the cube grows to infinity. We prove that, with probability one in the large volume...
Spectral type of a polynomial of stationary Gaussian process
Spectral type of some transformations of certain stochastic processes.
Spectrum decomposition for stationary weakly isotropic random fields with bounded range interactions
Spectrum of randomly sampled multivariate ARMA models
The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average (ARMA) models. We determine precisely the spectrum numerator coefficients of the randomly sampled ARMA models. We give results when the non-zero poles of the initial ARMA model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.
Speed of the Brownian loop on a manifold
We define the speed of the curved Brownian bridge as a white noise distribution operating on stochastic Chen integrals.
Spektralna karakteristika ekstrapolacije jedne klase stacionarnih slučajnih procesa
Spherical and hyperbolic fractional Brownian motion.
Spitzer's condition for random walks and Lévy processes
Splitting the conservation process into creation and annihilation parts
The aim of this paper is the study of a non-commutative decomposition of the conservation process in quantum stochastic calculus. The probabilistic interpretation of this decomposition uses time changes, in contrast to the spatial shifts used in the interpretation of the creation and annihilation operators on Fock space.
Spontaneous breaking of continuous rotational symmetry in two dimensions.