I am originally from Bristol and before joining the MASDOC programme I completed my MMath degree at the University of Warwick, achieving a first class with honours. I am (when I choose to be) a committed member of the university Athletics Club, having competed in the Warwick colours many times during my undergraduate degree.
My main mathematical interests lie within Probability theory. Specifically pertaining to random walks,interacting particle systems, percolation theory and (stochastic) partial differential equations. In particular, my research focuses primarily on systems of coalescing random walks in various contexts.
As part of the first year of the MASDOC programme, I undertook a summer research project that culminated in a masters dissertation. The title of the dissertation is "On the Asymptotic Density of an Infinite System of Coalescing Random Walks" and the work was supervised by Roger Tribe.
Abstract. An infinite system of particles in Zd is considered performing independent, continuous
time random walks that interact by immediately coalescing on collision. In
particular, we study the asymptotic behaviour of the occupation of fixed sites. A
review is made of the heuristic arguments of van den Berg and Kesten (2000) for
the case of one fixed site in dimension greater than 2 where they are able to replicate the earlier result
of Bramson and Griffeath (1980). We apply the arguments to dimension less than 3 and we initiate
the adaptation of these techniques to multiple fixed sites in d = 2.
The lines of research of the master dissertation has been continued into the 2nd year of the programme supervised by Roger Tribe and Oleg Zaboronski.
I can be contacted by email through the address j dot lukins at warwick dot ac dot uk. Or in the office B3.04.