Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2001-09-17
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.
Hastings Matthew B.
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