135 research outputs found
Random Operator Approach for Word Enumeration in Braid Groups
We investigate analytically the problem of enumeration of nonequivalent
primitive words in the braid group B_n for n >> 1 by analysing the random word
statistics and the target space on the basis of the locally free group
approximation. We develop a "symbolic dynamics" method for exact word
enumeration in locally free groups and bring arguments in support of the
conjecture that the number of very long primitive words in the braid group is
not sensitive to the precise local commutation relations. We consider the
connection of these problems with the conventional random operator theory,
localization phenomena and statistics of systems with quenched disorder. Also
we discuss the relation of the particular problems of random operator theory to
the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl.
Phys. B [PM
Some Aspects of Multifractal analysis
The aim of this survey is to present some aspects of multifractal analysis
around the recently developed subject of multiple ergodic averages. Related
topics include dimensions of measures, oriented walks, Riesz products etc
Random ballistic growth and diffusion in symmetric spaces
Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN)
interactions in a N-column box is viewed a time-ordered product of N\times
N-matrices consisting of a single sl_2-block which has a random position along
the diagonal. We relate the uniform BD growth with the diffusion in the
symmetric space H_N=SL(N,R)/SO(N). In particular, the distribution of the
maximal height of a growing heap is connected with the distribution of the
maximal distance for the diffusion process in H_N. The coordinates of H_N are
interpreted as the coordinates of particles of the one--dimensional Toda chain.
The group-theoretic structure of the system and links to some random matrix
models are also discussed.Comment: 29 pages, 7 figures. Revised and published version. To appear in
Nuclear Physics
Phylogeography of the Spanish Moon Moth Graellsia isabellae (Lepidoptera, Saturniidae)
Excited-State Dynamics of Hybrid Multichromophoric Systems: Toward an Excitation Wavelength Control of the Charge Separation Pathways
A Close Look at Charge Generation in Polymer:Fullerene Blends with Microstructure Control
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