Related papers: Bohmian transmission and reflection dwell times wi…
We are concerned with the justification of the statement, commonly (explicitly or implicitly) used in quantum scattering theory, that for a free non-relativistic quantum particle with initial wave function $\Psi_0(\boldsymbol{x})$,…
Let $B=(B_t)_{t\in {\mathbb{R}}}$ be a two-sided standard Brownian motion. An unbiased shift of $B$ is a random time $T$, which is a measurable function of $B$, such that $(B_{T+t}-B_T)_{t\in {\mathbb{R}}}$ is a Brownian motion independent…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
We show that residence time measure can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one--dimensional simple random walk. The sites of the lattice are regular,…
Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of trajectories has remained difficult to assess. Such assessment is critical not only for establishing the…
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…
Inspired by Mott's (1929) analysis of particle tracks in a cloud chamber, we consider a simple model for quantum cosmology which includes, in the total Hamiltonian, model detectors registering whether or not the system, at any stage in its…
Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to math finance, and under general stability conditions, it has a unique stationary distribution.…
We introduce a novel concept of simple loop dwell time and use it to give sufficient conditions for stability of a continuous-time linear switched system where switching between subsystems is governed by an underlying graph. We present a…
We report a detailed and systematic study of wave propagation through a stochastic absorbing random medium. Stochastic absorption is modeled by introducing an attenuation constant per unit length $\alpha$ in the free propagation region of…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
Consider an multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this…
We study the transmission and group delay time for fermions in graphene under a proximity exchange field scattered by double barriers. Solving the Dirac equation over five regions, we calculate transmission and reflection coefficients using…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
Route-level travel time reliability requires characterizing the distribution of total travel time across correlated segments -- a problem where existing methods either assume independence (fast but miscalibrated) or model dependence via…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…