ISSN:
1572-9613
Keywords:
random walk
;
large deviations
;
persistence
;
algebraic functions
;
periodic critical amplitudes
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the one-dimensional lattice random walk in discrete time. We determine the survival probability of the random walker in the presence of an obstacle moving ballistically with velocity v, i.e., the probability that the random walker remains up to time n on the left of the obstacle. Three regimes are to be considered for the long-time behavior of this probability, according to the sign of the difference between v and the drift velocity V¯ of the random walker. In one of these regimes (v〉V¯), the survival probability has a nontrivial limit at long times which is discontinuous at all rational values of v. An algebraic approach allows us to compute these discontinuities as well as several related quantities. The mathematical structure underlying the solvability of this model combines elementary number theory, algebraic functions, and algebraic curves defined over the rationals.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1004636216365
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