publication . Article . Preprint . 2012

From elongated spanning trees to vicious random walks

V. B. Priezzhev; Sergei Nechaev; Sergei Nechaev; V. S. Poghosyan; Alexander Gorsky;
Open Access English
  • Published: 14 Jun 2012
  • Publisher: HAL CCSD
  • Country: France
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 in a fashion 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 $r^{-\nu} \log r$ with $\nu = (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see that the two--dimensional $k$--leg loop--erased watermelon exponent $\n...
Subjects
free text keywords: [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Nuclear and High Energy Physics, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory, Mathematical Physics, Random walk, Physics, Correlation function, Exponent, Integrable system, Large distance, Combinatorics, Scaling, Square lattice, Spanning tree
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