Combinatorics of stretched 2D loop-erased random walks

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• Dr Sergei Nechaev, Université Paris-Sud, France
• Thursday 07 June 2012, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Dr Dimitri M Gangardt.

We consider by combinatorial methods the correlation function of k (k is odd) loop-erased random walks in 2D. Starting and ending points of the paths are grouped in a fashion of a k-leg watermelon. For large distance between watermelon extremities, the reunion exponent is (k^2 - 1)/2, in coincidence with known CFT result. Elongating the loop-erased random walks in some direction, we examine how the reunion exponent of k loop-erased random walks is converting into the reunion exponent of k vicious walkers (i.e. world lines of free fermions in (1+1)D). The considered model allows to speculate how by changing the degree of stretching, one can interpolate from the logarithmic Conformal Field Theory to the Random Matrix Theory.

This talk is part of the Theoretical Physics Seminars series.

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