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.
The programme will include a number of lectures and public talks by distinguished fellows associated with the programme:
The organizers gratefully acknowledge the support of the Clay Mathematics Institute.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Stochastic systems for anomalous diffusion, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.
8 July 2024 to 12 July 2024
5 August 2024 to 9 August 2024
4 September 2024 to 6 September 2024
28 October 2024 to 1 November 2024
25 November 2024 to 29 November 2024
Subscribe for the latest updates on events and news
INI is a creative collaborative space which is occupied by up to fifty-five mathematical scientists at any one time (and many more when there is a workshop). Some of them may not have met before and others may not realise the relevance of other research to their own work.
INI is especially important as a forum where early-career researchers meet senior colleagues and form networks that last a lifetime.
Here you can learn about all activities past, present and future, watch live seminars and submit your own proposals for research programmes.
Within this section of the website you should find all the information required to arrange and plan your visit to the Institute. If you have any further questions, or are unable to find the information you require, please get in touch with the relevant staff member or our Reception team via our contact pages.
INI and its programme participants produce a range of publications to communicate information about activities and events, publish research outcomes, and document case studies which are written for a non-technical audience. You will find access to them all in this section.
The Isaac Newton Institute aims to maximise the benefit of its scientific programmes to the UK mathematical science community in a variety of ways.
Whether spreading research opportunities through its network of correspondents, offering summer schools to early career researchers, or hosting public-facing lectures through events such as the Cambridge Festival, there is always a great deal of activity to catch up on.
Find out about all of these endeavours in this section of the site.
There are various ways to keep up-to-date with current events and happenings at the Isaac Newton Institute. As detailed via the menu links within this section, our output covers social media streams, news articles, a regular podcast series, an online newsletter, and more detailed documents produced throughout the year.
“A world famous place for research in the mathematical sciences with a reputation for efficient management and a warm welcome for visitors”
The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
INI has a vital national role, building on many strengths that already exist in UK universities, aiming to generate a new vitality through stimulating and nurturing research throughout the country.During each scientific programme new collaborations are made and ideas and expertise are exchanged and catalysed through lectures, seminars and informal interaction, which the INI building has been designed specifically to encourage.
For INI’s knowledge exchange arm, please see the Newton Gateway to Mathematics.
The Institute depends upon donations, as well as research grants, to support the world class research undertaken by participants in its programmes.
Fundraising activities are supported by a Development Board comprising leading figures in academia, industry and commerce.
Visit this section to learn more about how you could play a part in supporting INI’s groundbreaking research.
In this section you can find contact information, staff lists, maps and details of how to find INI’s main building in Cambridge.
Our administrative staff can help you with any queries regarding a prospective or planned visit. If you would like to discuss a proposed a research programme or other event, our senior management team will be happy to help.