Stochastic Resetting and Its Associated Costs

by Mr John Chakanal Sunil (University of Edinburgh)

Thursday 15 Jan 2026, 11:30 → 12:30 Asia/Kolkata

A 304 and on zoom

Abstract:

Searching for misplaced objects is a task that we are all familiar with. In particular, the way we search for a misplaced object, such as keys, is by repeatedly resetting to the object’s last known location. It has been shown that such resetting expedites the mean time to complete the search process. However, in practice, resets must also incur costs, whether in time, energy, or money. This motivates examining the typical cost for the process as well as the probabilities of rare cost fluctuations that deviate significantly from the typical behaviour.

In this talk, I will demonstrate the effect of costly resets and the large deviations exhibited by the tails of the total cost distribution using an exactly solvable model known as "Diffusion with Stochastic Resetting". Further, I will discuss the eventual breakdown of the large deviation principle for certain classes of cost functions, resulting in a phase transition known as condensation.

References:

M. R. Evans, S. N. Majumdar, and G. Schehr, “Stochastic resetting and applications”, J. Phys. A, vol. 53, p. 193001, 2020.
J. C. Sunil, R. A. Blythe, M. R. Evans, and S. N. Majumdar, “The cost of stochastic resetting”, J. Phys. A, vol. 56, p. 395001, 2023.
M. R. Evans and J. C. Sunil, “Stochastic Resetting and Large Deviations”, SciPost Phys. Lect. Notes, vol. 103, 2025.