Related papers: On Woolhouse's Cotton-Spinning Problem
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…
The actual progression of pitting on ball screw drive spindles is not well known since previous studies have only relied on the investigation of indirect wear effects (e. g. temperature, motor current, structure-borne noise). Using images…
In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The change occurs at an unknown "disorder" time with exponential…
The sequential sampling of populations with unequal probabilities and with replacement in a closed population is a recurrent problem in ecology and evolution. Many of these questions can be reformulated as urn problems, often as special…
An increasing number of electronics are directly embedded on the clothing to monitor human status (e.g., skeletal motion) or provide haptic feedback. A specific challenge to prototype and fabricate such a clothing is to design the wiring…
An overview is presented of recent work on some statistical problems on multiparticle random walks. We consider a Euclidean, deterministic fractal or disordered lattice and N >> 1 independent random walkers initially (t=0) placed onto the…
In 1996, Bertoin and Werner [5] demonstrated a functional limit theorem, characterising the windings of pla- nar isotropic stable processes around the origin for large times, thereby complementing known results for planar Brownian mo- tion.…
The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture…
We investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v. For the continuous-time problem (Brownian motion), we provide a simple alternative proof of Newman's recent…
Order picking is the problem of collecting a set of products in a warehouse in a minimum amount of time. It is currently a major bottleneck in supply-chain because of its cost in time and labor force. This article presents two exact and…
The Abstract Milling problem is a natural and quite general graph-theoretic model for geometric milling problems. Given a graph, one asks for a walk that covers all its vertices with a minimum number of turns, as specified in the graph…
Many problems in finance are related to first passage times. Among all of them, we chose three on which we contributed personally. Our first example relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way that tail…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is…
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by M. Birnkenr et.al. Each particle performs simple random walk…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
Empirical, theoretical and historical aspects of Post's "problem of tag" from 1921 are explored. Evidence of strong computational irreducibility is found. Despite their deterministic origin, the lengths of successive sequences generated…