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- W2288278889 abstract "The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a single loop renormalised perturbation theory of a stochastic process closely related to the Wiener Sausage, which, however, proves to be exact for the exponents and some amplitudes. The field-theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem. While we recover a number of known, classical results, the field-theoretic techniques deployed provide a particularly versatile framework, which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions. At the same time, we provide a highly instructive, non-trivial example for some of the technical particularities of the field-theoretic description of stochastic processes, such as excluded volume, lack of translational invariance and immobile particles. The aim of the present work is not to improve upon the well-established results for the Wiener Sausage, but to provide a field-theoretic approach to it, in order to gain a better understanding of the field-theoretic obstacles to overcome." @default.
- W2288278889 created "2016-06-24" @default.
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- W2288278889 date "2016-03-09" @default.
- W2288278889 modified "2023-09-27" @default.
- W2288278889 title "A Field-Theoretic Approach to the Wiener Sausage" @default.
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- W2288278889 doi "https://doi.org/10.1007/s10955-016-1483-2" @default.
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