First-passage times and queueing behavior of stochastic search with dynamic redundancy and mortality

Friday, 19 June 2026, 11am to 12pm

Stochastic search is ubiquitous in biology and ecology, from synaptic transmission and intracellular signaling to predators seeking prey and the spread of disease. In dynamic systems like these, the number of 'searchers' is rarely constant: new agents may be recruited while others can abandon the search. Despite the ubiquity of these dynamics, their combined influence on search times remains largely unexplored. In this talk we will introduce a general framework for stochastic search in which agents progressively join and leave the process, a mechanism we term 'dynamic redundancy and mortality'. Under minimal assumptions on the underlying search dynamics, our framework yields the exact distribution of the first-passage time to a target region and further reveals surprising connections to stochastic search with stochastic resetting, wherein a single searcher is randomly 'reset' to its initial state. We will then treat the target region as a queue, which we show has interarrival times governed by a thinned nonhomogeneous Poisson process. Altogether this work provides a rigorous foundation for studying stochastic search processes with a fluctuating number of searchers. This work is in collaboration with Dr. Aanjaneya Kumar (Santa Fe Institute) and José Giral-Barajas (Imperial College London).

Speaker(s): Dr Samantha Linn (Department of Mathematics, Imperial College, London)

Series: Mathematical Biology and Ecology Seminar Series

Venue: Mathematical Institute - L4 - L4 Mathematical Institute Woodstock Road Oxford Oxfordshire OX2 6GG United Kingdom

Department: Mathematical Institute (Department)

Organiser: Sara Jolliffe

Host: Dr Giulia Celora