Objective In this proposal we aim at studying the dynamic properties of systems that evolve in time according to some local random mechanism.We focus on three types of systems: mobile point processes, allocation via sandpiles and random triangulations.For mobile point processes, we considera Poisson point process of particles that move as independent continuous-time random walks on Z^2. Thismodel has been studied as an abstraction to mobile wireless networks and moving populations. Our goal is to study the problem of whether a target can escape detection by the particles, how fast an aggregate can grow by gluing particles on its surface, and how the environments can affect the performance of mobile particles.For allocation via sandpiles, we consider the following model for allocation n particles on the vertices of a graph.Particles arrive one a time and, when a particle arrives, it first chooses a vertex u uniformly at random. Then the particle performs a local search starting from u until it reaches a vertex with a local minimum pile of particles, where the particle is finally placed. We study how balanced the pile of particles are and the behavior of this process on infinite graphs, especially in connection with sandpile models.For random triangulations, we consider the n x n square lattice and study the so-called flip dynamics, a Markov chain over triangulations of this point set that is of interest to researchers in combinatorics and computer graphics. Inthis dynamics, an edge is chosen uniformly at random and, if that edge lies inside a strictly convex quadrilateral, the edge isflipped to the opposite diagonal of the quadrilateral. Our goal is to understand the mixing time of this structure as n goes toinfinity and to understand non-stationary properties of this system, such as the time it takes until all edges of thetriangulation are smaller than some given value. Fields of science natural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2013-CIG - Marie-Curie Action: "Career Integration Grants" Call for proposal FP7-PEOPLE-2013-CIG See other projects for this call Funding Scheme MC-CIG - Support for training and career development of researcher (CIG) Coordinator UNIVERSITY OF BATH EU contribution € 75 000,00 Address CLAVERTON DOWN BA2 7AY Bath United Kingdom See on map Region South West (England) Gloucestershire, Wiltshire and Bristol/Bath area Bath and North East Somerset, North Somerset and South Gloucestershire Activity type Higher or Secondary Education Establishments Administrative Contact Hazel Wallis (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
