Stochastic systems for anomalous diffusion
SSD
1 July 2024 to 18 December 2024
Programme theme
Diffusion refers to the movement of a particle or larger object through space subject to random effects. Mathematical models for diffusion phenomena give rise to stochastic processes, including classes of processes known collectively as diffusions or random walks. Such processes are ubiquitous in stochastic modelling single-particle or many-particle systems in physics (conformation of polymer molecules, mass transport, etc.), ecology (foraging, migration, dispersal, etc.), biology (microbe locomotion, etc.), chemistry (surface science, etc.) and many other areas. Diffusions and random walks are also primary ingredients of stochastic sampling and optimization algorithms in computational statistics and machine learning.
Anomalous diffusion describes processes that exhibit behaviour deviating fundamentally from the simplest diffusion models. Various physical, biological, or social mechanisms can produce anomalous diffusion. For example, processes may interact in complex ways with their past evolution, e.g., in systems with feedback, learning, or resource depletion, or with their spatial environment, e.g., in spaces with boundary reflections, anisotropy, or other non-trivial structure. Boundary reflections can drive a process to accelerate or confine it; learning or adaptive dynamics can force a process to dissipate faster; environmental inhomogeneities can trap or slow down diffusion; these are all “anomalous” behaviours.
In applications, to access fresh resources, roaming animals prefer not to retrace their steps; the excluded volume effect in polymers ensures that no two monomers can occupy the same physical space; topographical, botanical, or chemical gradients in an environment lend a preferred direction to an organism’s motion. For statistical sampling and learning, processes that explore space faster than ordinary diffusions, or that adapt their behaviour according to previous learning, can lead to more efficient algorithms. Mathematical phenomena that are to be explored for processes exhibiting anomalous diffusion include limit behaviour, scaling limits, geometry and occupation statistics, mixing, and so on. Analysis of such processes can call on a range of tools from probability theory and stochastic analysis.
The programme will bring together researchers in probability, stochastic analysis, and related areas, as well as (through applications of anomalous diffusion) mathematical physicists, ecologists, and materials scientists, and (through sampling algorithms) researchers in computational statistics and machine learning. The programme is built around thematically linked workshops, and will be supported by seminar series, problem sessions, engagement events, and a social programme.
Workshops
Self-interacting processes
8 July 2024 to 12 July 2024
Geometry, occupation fields, and scaling limits
28 October 2024 to 1 November 2024
Adaptive and constrained sampling algorithms
25 November 2024 to 29 November 2024
Organisers
- Codina Cotar University College London
- Aleksandar Mijatovic University of Warwick; The Alan Turing Institute
- Anastasia Papavasiliou University of Warwick
- Ellen Powell Durham University
- Kavita Ramanan Brown University
- Kilian Raschel CNRS (Centre national de la recherche scientifique); Université d'Angers
- Perla Sousi University of Cambridge
- Andrew Wade Durham University
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