A field theory for the Wiener Sausage

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• Gunnar Pruessner, Imperial Mathematics
• Thursday 19 November 2015, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

The Wiener Sausage is a classic problem in probability theory that has been famously studied by Kolmogorov and Leontovich in 1933, as well as by a number of other very well known scientists, such as Spitzer, Kac and Luttinger, over the past one hundred years or so. The aim is to determine the moments of the volume traced out by a sphere attached to a Brownian particle. In the present work, I study the Wiener Sausage as a reaction diffusion process whose relevant observable follows the same limiting distributing as the original Wiener Sausage. That process allows for a treatment using renormalised field theory which I am going to present. The field theoretic approach is appealingly elegant and flexible, allowing for boundary conditions and the properties of the underlying lattice to be changed very easily, as well as for very simple implementation of variations of the process, such as introducing branching. Contrasting and comparing the present results with those about the Wiener Sausage in the literature also elucidates some of the deeper structure of field theory, such as the meaning of diagrams, momentum conservation and the implementation of hard core repulsion and immobile particles.

This talk is part of the Theoretical Physics Seminars series.

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