03 Dec 2021

Postdoctoral Fellowship in Special Functions and Random Walks at Basque Center for Applied Mathematics – BCAM

“Inside the Generalized Master Equation for the Continuous-Time Random Walk”
The proposed research project is focused on the derivation of the Generalized Master Equation (GME) for the Continuous-Time Random Walk (CTRW) as published in literature, e.g., [1,2], and on its specific determination for fractional diffusion [3]. Actually, the GME depends on a kernel function that is explicitly given in terms of the jumps and waiting-times distributions of the CTRW. Surprisingly, a systematic study concerning the features of the CTRW, the kernel of the GME and the resulting walker’s distribution is not provided, yet. The aim of the research is to fill this literature gap in the view of the many applications of the CTRW and in particular because of the recent regime-transitions (exponential-to-fractional-to-Gaussian) observed in anomalous diffusion processes.
[1] Klafter J and Silbey R 1980 Phys. Rev. Lett. 44 55–58
[2] Klafter J, Blumen A and Shlesinger M F 1987 Phys. Rev. A 35 3081–3085
[3] Hilfer R and Anton L 1995 Phys. Rev. E 51 R848–R851
Contract and offer: 1 year + 1 year
Requirements: Applicants must have their PhD completed before the contract starts.
Deadline for application: January 17, 2021
For further information and applications: http://www.bcamath.org/en/research/job/ic2021-11-postdoctoral-fellowship-in-special-functions-and-random-walks