Agrawal, Himanshu ; Dhar, Deepak (2002) Probability distribution of the sizes of the largest erased loops in looperased random walks Physical Review E, 65 (3). 031108_1031108_8. ISSN 1063651X

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Official URL: http://pre.aps.org/abstract/PRE/v65/i3/e031108
Related URL: http://dx.doi.org/10.1103/PhysRevE.65.031108
Abstract
We have studied the probability distribution of the perimeter and the area of the kth largest erased loop in looperased random walks in two dimensions for k=1 to 3. For a random walk of N steps, for large N, the average value of the kth largest perimeter and area scales as N^{5/8} and N, respectively. The behavior of the scaled distribution functions is determined for very large and very small arguments. We have used exact enumeration for N ≤20 to determine the probability that no loop of size greater than l is erased. We show that correlations between loops have to be taken into account to describe the average size of the kth largest erased loops. We propose a onedimensional Levy walk model that takes care of these correlations. The simulations of this simpler model compare very well with the simulations of the original problem.
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ID Code:  9306 
Deposited On:  02 Nov 2010 12:31 
Last Modified:  16 May 2016 19:07 
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