Related papers: On quasi-ergodic distribution for one-dimensional …
The convex closure of entropy vectors for quasi-uniform random vectors is the same as the closure of the entropy region. Thus, quasi-uniform random vectors constitute an important class of random vectors for characterizing the entropy…
We discuss the quantum geometric contribution to the diffusion constant and the DC conductivity in metals and semimetals with linear Dirac dispersion. We demonstrate that, for systems with perfectly linear dispersion, there exists a clear…
We consider the classical Shiryaev--Roberts martingale diffusion, $(R_t)_{t\ge0}$, restricted to the interval $[0,A]$, where $A>0$ is a preset absorbing boundary. We take yet another look at the well-known phenomenon of quasi-stationarity…
We have considered a semi-infinite crack embedded in a transversely isotropic medium and studied two special cases, one, in which the axis of symmetry is normal to the crack face and the wave incidence is arbitrary and another, in which the…
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process…
In this paper, we study a special class of quasi-homomorphisms, i.e. quasi-retractions from a group to its subgroups. We first give some algebraic and geometric properties of quasi-retracts and then propose a theory of quasi-split short…
In this note, we discuss the uniform ergodicity of a diffusion process given by an It\^o stochastic differential equation. We present an integral condition in terms of the drift and diffusion coefficients that ensures the uniform ergodicity…
We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Ergodic many-body systems are expected to reach quasi-thermal equilibrium. Here we demonstrate that, surprisingly, high-energy electrons, which are injected into a quantum Hall edge mode with finite range interactions, stabilize at a…
As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well-defined since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the…
We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…
The explicit criteria for several types of ergodicity of one-dimensional diffusions or birth-death processes have been found out recently in a surprisingly short period. One of the criteria is for exponential ergodicity of birth-death…
Quantum-confined semiconductor structures are the cornerstone of modern-day electronics. Spatial confinement in these structures leads to formation of discrete low-dimensional subbands. At room temperature, carriers transfer among different…
Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for…
This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…
We have studied the diffusion of excess quasiparticles in a current-biased superconductor strip in proximity to a metallic trap junction. In particular, we have measured accurately the superconductor temperature at a near-gap injection…
We construct a quasi likelihood analysis for diffusions under the high-frequency sampling over a finite time interval. For this, we prove a polynomial type large deviation inequality for the quasi likelihood random field. Then it becomes…
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…