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- W2019998505 abstract "Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of k paths (k is odd) along branches of trees or, equivalently, k loop-erased random walks. Starting and ending points of the paths are grouped such that they form a k-leg watermelon. For large distance r between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as r−νlogr with ν=(k2−1)/2. Considering the spanning forest stretched along the meridian of this watermelon, we show that the two-dimensional k-leg loop-erased watermelon exponent ν is converting into the scaling exponent for the reunion probability (at a given point) of k (1+1)-dimensional vicious walkers, ν˜=k2/2. At the end, we express the conjectures about the possible relation to integrable systems." @default.
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- W2019998505 date "2013-05-01" @default.
- W2019998505 modified "2023-10-15" @default.
- W2019998505 title "From elongated spanning trees to vicious random walks" @default.
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- W2019998505 doi "https://doi.org/10.1016/j.nuclphysb.2013.01.003" @default.
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