Partial and random lattice covering times in two dimensions
- 13 June 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 72 (24) , 3745-3749
- https://doi.org/10.1103/physrevlett.72.3745
Abstract
The problems of the partial covering time (PCT) and of the random covering time (RCT) are studied in two dimensions using Monte Carlo simulations. We find that the PCT (RCT) presents a discontinuous transition at f=1 (f=0), where f is the fraction of visted sites by a random walker. An analysis of the time evolution of the surviving unvisited clusters reveals that they exhibit a time-dependent fractal-like structure.Keywords
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