R. D'Hulst, G. J. Rodgers
Published 2001-05-09Version 1
A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We establish a link between these properties and determine two transitions for each property, a percolation transition and a depinning transition. If the adaptation process is iterated, the antipersistent state becomes an attractor of the dynamics. Extensions to higher dimensions are briefly discussed.
Comments: 4 pages, 4 figures, submitted to publication
Theoretical bound of the efficiency of learning
Joint distribution of two Local Times for diffusion processes with the application to the construction of various conditioned processes
Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
