相关论文: Power law dependence in a random differential equa…
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…
Even though the phenomenological relations between perception and stimulus have been firmly established, a theoretical argument for Weber's and Fechner's law in terms of relevant models or from statistical physics is largely missing. We…
We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
The studied model describes a particle that obeys a one-dimensional nonlinear Schr\"odinger equation in the potential of a double-well. Transitions between the two lowest self-trapped states of this system under the influence of the…
We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a…
This paper deals with an analysis and design of robust, state-feedback control law uniform-asymptotically stabilizing at origin the system consisting of coupled $n$th--order ordinary differential equations in the presence of a non-vanishing…
It is well known that random multiplicative processes generate power-law probability distributions. We study how the spatio-temporal correlation of the multipliers influences the power-law exponent. We investigate two sources of the time…
We investigate the equilibration of a small isolated quantum system by means of its matrix of asymptotic transition probabilities in a preferential basis. The trace of this matrix is shown to measure the degree of equilibration of the…
Heterogeneous diffusion with spatially changing diffusion coefficient arises in many experimental systems like protein dynamics in the cell cytoplasm, mobility of cajal bodies and confined hard-sphere fluids. Here, we showcase a simple…
In this article, results from the previous paper (I) are applied to calculations of squeezed states for such well-known systems as the harmonic oscillator, free particle, linear potential, oscillator with a uniform driving force, and…
At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence, and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among…
We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected…
We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The…
In this paper, we consider the sublinear expectation on bounded random variables. With the notion of uncorrelatedness for random variables under the sublinear expectation, a weak law of large numbers is obtained. With the notion of…
Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…
This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…
We investigate the influence of the vacuum fluctuations of a background electric field over a charged test particle in the presence of a perfectly reflecting flat wall. A switching function connecting different stages of the system is…
We study the relaxation of a Brownian particle with long range memory under confinement in one dimension. The particle diffuses in an arbitrary confining potential and resets at random times to previously visited positions, chosen with a…