Related papers: Captive Jump Processes
To spontaneously break their intrinsic symmetry and self-propel at the micron scale, isotropic active colloidal particles and droplets exploit the non-linear convective transport of chemical solutes emitted/consumed at their surface by the…
We consider dynamics of the empirical measure of vertex neighborhood states of Markov interacting jump processes on sparse random graphs, in a suitable asymptotic limit as the graph size goes to infinity. Under the assumption of a certain…
Let $\Gamma$ denote the space of all locally finite subsets (configurations) in $R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\Gamma$ in which pairs of particles simultaneously hop over $R^d$. In this…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
We use colloidal suspensions encapsulated in emulsion droplets to model confined glass-forming liquids with tunable boundary mobility. We show dynamics in these idealized systems are governed by physical interactions with the boundary.…
Brownian dynamics play a key role in understanding the diffusive transport of micro particles in a bounded environment. In geometries containing confining walls, physical laws determine the behavior of the random trajectories at the…
Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…
When the unconditioned process is a diffusion living on the half-line $x \in ]-\infty,a[$ in the presence of an absorbing boundary condition at position $x=a$, we construct various conditioned processes corresponding to finite or infinite…
We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
We report an experimental investigation of the caging motion in a uniformly heated granular fluid, for a wide range of filling fractions, $\phi$. At low $\phi$ the classic diffusive behavior of a fluid is observed. However, as $\phi$ is…
We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the…
We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behaviour of…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
We apply wave packet methods to study an ion-trap system in the strong excitation regime imposing neither the rotating wave nor the Lamb-Dicke approximations. By this approach we show the existence of states with restricted phase space…
We study the large time behavior of the survival probability $\mathbb{P}_x\left(\tau_D>t\right)$ for symmetric jump processes in unbounded domains with a positive bottom of the spectrum. We prove asymptotic upper and lower bounds with…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…