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We study the order statistics of one dimensional branching Brownian motion in which particles either diffuse (with diffusion constant $D$), die (with rate $d$) or split into two particles (with rate $b$). At the critical point $b=d$ which…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
We study a set of Run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation {\theta} of the particle can assume a set of n possible discrete values while in the second case {\theta} is a…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $< x^2(t) >\propto t$, while anomalous behavior is expected to show a different time dependence, $ < x^2(t) > \propto…
We present a first numerical investigation of the accuracy of the recently proposed {\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
Reliable quantification of epistemic and aleatoric uncertainty is of crucial importance in applications where models are trained in one environment but applied to multiple different environments, often seen in real-world applications for…
Using a probabilistic neural network and Lagrangian observations from the Global Drifter Program, we model the single particle transition probability density function (pdf) of ocean surface drifters. The transition pdf is represented by a…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
The statistical properties of the $E \times B$ flux in different types of plasma turbulence simulations are investigated using probability density distribution functions (PDF). The physics included in the models ranges from two dimensional…
The manner in which probability amplitudes of paths sum up to form wave functions of orbital angular momentum eigenstates is described. Using a generalization of stationary-phase analysis, distributions are derived that provide a measure of…
In fluid dynamics experiments, flake-based flow visualization is a common technique to capture flow structures through the rays reflected from flat tracers suspended in the fluid. However, the correspondence between light intensity patterns…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions.…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to…