07 September 2022
ICTS graduate student Prashant Singh’s work, done together with his advisor Anupam Kundu, has been selected for the Top Cited Paper Awards India 2022 in the mathematical sciences category by IOP Publishing.
The publication, titled ‘Generalised ‘Arcsine’ Laws for Run-and-Tumble Particle in One Dimension,’ appeared in the Journal of Statistical Mechanics –Theory and Experiment. For a particle exhibiting random motion, Arcsine laws refer to the properties of the following three quantities: (a) time at which maximum position is attained, (b) total duration for which the position is positive, and (c) last time the position changes its sign from positive to negative or negative to positive. These quantities characterize the spatio-temporal properties of the trajectories. Paul Levy, in 1940, proved that for a one-dimensional Brownian motion, the probability distributions of these three seemingly disparate quantities are the same and given by a simple arcsine function. Prashant and Anupam explored the arcsine laws in the context of an archetypical model of bacteria called the run and tumble model. Their study established the exact conditions under which the universality of these laws can be established for this particular model. More information on this work can be found here.