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The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
The run-and-tumble particle (RTP) is one of the simplest examples of an active particle in which the direction of constant motion randomly switches. In the one-dimensional (1D) case this means switching between rightward and leftward…
Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…
We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding…
We study stochastic bifurcation for a system under multiplicative stable Levy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states in its most probable phase portraits. We have found…
Stochastic trajectory optimisation under uncertainty requires robust constraint satisfaction through chance constraints. However, existing transcription methods remain limited to scalar constraints or highly specific structures while…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
While the absorption of light is ubiquitous in nature and in applications, the question remains how absorption modifies the transmission channels in random media. We present a numerical study on the effects of optical absorption on the…
We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement…
In a recent article, Krapivsky and Redner (J. Stat. Mech. 093208 (2018)) established that the distribution of the first hitting times for a diffusing particle subject to hitting an absorber is independent of the direction of the external…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work we show how these dynamics can be…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
We study the diffusive dynamics of a hard-sphere fluid confined between parallel smooth hard walls. The position-dependent diffusion coefficient normal to the walls is larger in regions of high local packing density. High density regions…
Pulsatile fluid flows through straight pipes undergo a sudden transition to turbulence that is extremely difficult to predict. The difficulty stems here from the linear Floquet stability of the laminar flow up to large Reynolds numbers,…
We provide probabilistic interpretation of resonant states. This we do by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of…
We investigate the evolution of the quantum state for a free particle placed into a random external potential of white-noise type. The master equation for the density matrix is derived by means of path integral method. We propose an…
We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or Ising $p$-spin glass model, and (b)…
We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its…
We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system leave prescribed regions of the state…