Non-local Correlation Functions in a Spanning Trees Near the Boundary

Student: Nurligareev Khaydar

Educational Programme: Mathematics (Master)

Year of Graduation: 2018

Given a large square lattice with open boundary, we consider a correlation function of k loop-erased random walks with starting and ending points chosen such a way that the construction has a form of a k-leg watermelon. It turns out that for large distance r between the groups of starting and ending points the ratio of the number of watermelon configurations to the total number of spanning trees behaves as C · r^(−ν) with ν = k(k + 1). Using combinatorial methods, we prove this results and evaluate the constant C.

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