Ordinary and non-linear diffusion with stochastic resetting
Prof. Przemysław Chełminiak

Date, Time
06.10, 15:00 - 16:00

Location
Link to MSTeams meeting

Stochastic resetting – also known as restart – is a multidisciplinary scientific field which
recently attracted vigorous interest in such diverse disciplines as physics (coagulation-diffusion
processes), chemistry (enzymatic catalysis), biology (transcription factors-DNA interactions),
ecology (animal foraging for food), computer science (randomized algorithms), and even
economics and finances (stock-market dynamics). While most studies to date have been
theoretical, several experimental groups have now entered the playing field, which marks
the dawn of a new era.
A resetting protocol is a simple mechanism that stops a considered stochastic process at
random instants of time in order to return it to some pre-determined state, from which it starts
anew. Arguably, the most common and widely applied resetting protocol is ‘exponential resetting’,
which uses stochastic timers that are exponentially distributed. Specifically, in exponential
restart the resetting epochs follow Poisson statistics. The effect of exponential restart on the
dynamical and first-passage properties of stochastic processes was extensively studied mainly
for the ordinary diffusion. That is why, the purpose of the seminar is to present the aforementioned
issues from a viewpoint of the non-linear diffusion. In this context, the following will be considered:
– influence of exponential resetting on the mean square displacement and the probability density
function,
– optimization of the first-passage time statistics, and
– universal property of relative fluctuation in the optimized mean first-passage time.

Literature:

M. R. Evans, S. N. Majumdar and G. Schehr, Stochastic resetting and applications,
J. Phys. A: Math. Theor. 53, 193001 (2020).
P. Chełminiak, Non-linear diffusion with stochastic resetting, J. Phys.A: Math. Theor. 55,
384004 (2022).