| Searches through a fractal distribution of prey "Converting Space into Time: Effective Medium Theory for Random Walks in Disordered Systems" and "Extinction of Biological Random Walkers: Analytical Theory for Bacteriaand Epidemics." Files Models of coupled thermodynamic transport a)concerns random walks in which you choose as a generating algorithm not coin tossing or other Bernoulli scheme but a deck of cards or shuffle a finite amount of numbers or alphabets. This algorithm gives rise to non-Markovian walks which are nonetheless exactly solvable and have many interesting features AND/OR b) exponential functionals of many independent random walks - independent Kesten variables, we recently made a lot of studies starting with our work with Sid Redner on an ultimate fate of a helix-coil transition of a heteropolymer. I contiunued with some analysis of different statistical properties a portfolio of Asian options. A) Diffusion driven erosion of discrete scale invariance: Weierstrass walks and critical phenomena A. Robledo, IFUNAM, Mexico, and S. Abe, Mye University, Japan We determine the explicit form of the diffusion equation associated to systems that exhibit discrete scale invariance as epitomized by the Weierstrass random walk. For these systems anomalous diffusion is expressed as an eigenvalue problem where the relevant operator is a fractional difference Laplacian in the complex plane and the eigenvalues are the singular structure functions with logarithmic oscillations described by dilation calculus. We illustrate some aspects of the formalism by specific reference to the Weierstrass random walk and discuss the approach to the continuous Levy-Gnedenko stationary distribution limit. To reveal a novel relationship between the diffusion process and critical phenomena, we consider the full universality class of the Weierstrass walk via a renormalization group transformation for which this particular walk is its nontrivial fixed point [1]. REFS: [1] A. Robledo, Phys. Rev. Lett. 83, 2289 (1999). B) Robledo, A., Woodhouse, L., Multiple trapping of random walkers on periodic space lattices, J. Stat. Phys. 19, 129 (1978). ``Recurrence and first-passage times for systems with many random walkers'' REF: D.P. Sanders & H. Larralde Europhys. Lett. 82(4), 40005 (2008) AND ``Normal and anomalous diffusion in chaotic billiards'' REF: D. P. Sanders arXiv:0808.2235 (Accepted for publication (Oct 2008): Rapid Communication, Phys. Rev. E) |
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