Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

Details Exact Multifractal Spectra for Arbitrary Laplacian Random Walks Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

2001-09-17

arxiv.org/abs/cond-mat/0109304v2

Phys. Rev. Lett. 88, 055506 (2002).

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 3 figures; references added, minor corrections

Scientific paper

10.1103/PhysRevLett.88.055506

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge $c\leq 1$, with $c$ related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.

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