Dr. S. C. Harris

Department of Mathematical Sciences


Probability
at Bath

Contact Details Teaching Research Interests Projects Papers

Research Interests

 

Picture of a simulated branching Brownian motion.

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Mathematical Interests

My general research interests lie in probability theory. I have a broad interest throughout this field, including modeling and applications of stochastic processes, although my research has tended to concentrated on the theoretical side. I also enjoy membership of Bath's Centre of Mathematical Biology where interesting probabilistic models of biological processes often come to light.

My main focus is on branching diffusions - which can roughly be thought of as models for populations of 'animals' which breed, die and move around in space. This work often involves the inter-play of probability with mathematical analysis through links with non-linear partial differential equations. For example, one aim has been to prove results about travelling-wave solutions of reaction-diffusion equations via probabilistic methods by studying corresponding branching diffusion models. Related models have been applied to diverse problems from chemical and physical reactions, population genetics and geology.

Some key words of interest are:

bulletMartingales, Markov processes and diffusions
bulletBrownian motion and stochastic calculus
bulletBranching processes
bulletBranching diffusions
bulletReaction-diffusion equations, FKPP equation.

Some typical problems of interest:

bullet Survival probabilities for BBM with killing at the origin
bullet Explosions in inhomogeneous branching potentials
bullet Speed of left-most particles in branching Markov processes
bullet Branching Brownian motion in an inhomogeneous potential
bullet Almost sure growth rates along paths within branching diffusions
bullet Large deviations along paths within branching diffusions
bullet A typed branching diffusion, reaction-diffusion equation and travelling-waves.
bullet Uniqueness of travelling-waves in reaction-diffusion equations
bullet Scaling random walks on random sets with random jump rates

 

 

Dr. Harris Univ of Bath Maths Dept Seminars Prob@Bath

Date page last edited: Wednesday January 09, 2008 13:22