EPSRC Reference: 
EP/M002896/1 
Title: 
Random Fractals 
Principal Investigator: 
Belyaev, Dr D 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Institute 
Organisation: 
University of Oxford 
Scheme: 
EPSRC Fellowship 
Starts: 
01 October 2014 
Ends: 
30 September 2019 
Value (£): 
847,723

EPSRC Research Topic Classifications: 
Mathematical Analysis 
Statistics & Appl. Probability 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
The proposed research is in Pure Mathematics, namely on the border of Complex Analysis, Probability, and Mathematical Physics. I will mostly study random fractal structures and use them to study important models of Statistical Physics. Fractals are selfsimilar structures that look the same at all places and on all scales. They appear everywhere in nature, notable examples are Romanesco broccoli, shorelines, lightnings, and sea shells. They also appear in many models of statistical physics that describe such phenomena as magnetism, flow of fluid through porous matter, spread of epidemics, robustness of networks and many others. One of the fundamental parameters of fractal structures is the dimension. Roughly speaking it describes the growth rate of the fractal structures. For example a straight interval of diameter N, which is made of the particles of unit size, contains N particles. We say that the interval has dimension 1. The square of size N contains N squared particles and has dimension 2. The characteristic property of fractal structures is that the structure of size N contains approximately N^d particles where 1 Except fractals that appear from physics lattice models, similar fractals are important in various areas of pure mathematics. A notable example is the area of mathematics which is called Complex Analysis. It turned out that the objects that maximize various quantities of interest must be of fractal nature. It turned out that it is very difficult to study these fractals since we don't have a good description of their structure. Here randomness comes into play in a seemingly paradoxical way: we introduce artificial randomness to simplify computations.
The proposed research will develop novel methods to study and describe growing random structures and apply these methods to fractals that appear in Analysis, Probability, and Mathematical Physics.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 

Further Information: 

Organisation Website: 
http://www.ox.ac.uk 