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We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial…
We will construct a theory which can explain the dynamics toward the steady state self-gravitating systems (SGSs) where many particles interact via the gravitational force. Real examples of SGS in the universe are globular clusters and…
We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to include spatially inhomogeneous activity. The method is applied to predict the…
Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…
When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Using Transportation Cost Inequalities for stochastic…
Context: Typical space plasmas contain spatially and temporally variable turbulent electromagnetic fields. Understanding the transport of energetic particles and the acceleration mechanisms for charged particles is an important goal of…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions…
Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…
A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression…
We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…
We propose a new stochastic model involving state-dependent variable exponent $p(\cdot)$ which allows modeling of systems where noise intensity adapts to the current state. This new flexible theoretical framework generalizes both the…
We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field,…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…