Related papers: Reactive trajectories and the transition path proc…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
Consider the multidimensional SDE $\mathrm d X(t) = a(X(t))\mathrm d t + b(X(t))\mathrm d W(t).$ We study the asymptotic behavior of its solution $X(t)$ as $t \to \infty$, namely, we study sufficient conditions of transience of its solution…
Activated transitions have rates that are often exponentially small in system size. Extracting the associated activation barriers is challenging in practice, especially in the deeply metastable regimes and in the presence of disorder. Here,…
A multi-type continuous state and continuous time branching process with immigration satisfying some moment conditions is identified as a pathwise unique strong solution of certain stochastic differential equation with jumps.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity…
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…
We propose alternatives to coupled-channels calculations with loosely-bound exotic nuclei (CDCC), based on the the random matrix (RMT) and the optical background (OPM) models for the statistical theory of nuclear reactions. The coupled…
Chemical reaction networks (CRNs) exhibit complex dynamics governed by their underlying network structure. In this paper, we propose a novel approach to study the dynamics of CRNs by representing them on species graphs (S-graphs). By…
Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
We apply the quantum-walk approach recently proposed in arXiv:quant-ph-1506.04213 to a radical-pair reaction where realistic estimates for the intermediate transition rates are available. The well-known average hitting time from quantum…
While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square…
The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in…
Starting from a classical mechanics of a ``colloid particle'' and $N$ ``water molecules'', we study effective stochastic dynamics of the particle which jumps between deep potential wells. We prove that the effective transition probability…
We study a class of kinetic-type differential equations $\partial \phi_t/\partial t+\phi_t=\widehat{\mathcal{Q}}\phi_t$, where $\widehat{\mathcal{Q}}$ is an inhomogeneous smoothing transform and, for every $t\geq 0$, $\phi_t$ is the…