Statistics Seminars: Random walk with barycentric self-interaction
6 January 2010 14:15 in CM221
The mathematical modelling of polymers in solution has produced some fascinating but hard problems, most notably the problem of the self-avoiding walk. The sites visited by the walk represent the locations of the monomers; the increments of the walk represent chemical bonds.
Heuristic arguments dating back to Nobel Laureate P.J. Flory in the 1940s predict the scaling behaviour of self-avoiding walk, but very little is known rigorously. The standard formulation of self-avoiding walk cannot be interpreted as a genuine stochastic process in the usual sense. It is of interest to formulate models for polymer molecules that are genuine stochastic processes. To retain the physical motivation, such processes must be self-interacting in some way, i.e., the stochastic evolution must depend upon the entire history of the process. This introduces challenges for analysis.
In this talk I will discuss a model introduced in collaboration with Francis Comets, Mikhail Menshikov, and Stas Volkov, whereby the intraction of a random walk with its previous history is mediated through the barycentre (centre of mass) of its previous trajectory. I will try to keep the talk fairly non-technical...!
Hosts: Iain MacPhee and Mikhail Menshikov
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