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DY: Fachverband Dynamik und Statistische Physik
DY 54: Statistical Physics: General II
DY 54.7: Vortrag
Donnerstag, 12. März 2026, 16:45–17:00, ZEU/0114
Emergence of generic first-passage time distributions for large Markovian networks — •Julian B. Voits1 and Ulrich S. Schwarz1,2 — 1Institute for Theoretical Physics, University of Heidelberg, Germany — 2BioQuant-Center for Quantitative Biology, University of Heidelberg, Germany
In many situations of practical interest, for example for decision-making in biological systems, it is sufficient to characterize a stochastic process by the time at which a final, absorbing state is reached (first-passage time). A prominent example is kinetic proofreading, where cells achieve remarkably accurate decisions through non-equilibrium reaction cycles. Earlier work studying corresponding models observed that as the system size grows, the first-passage time distributions converged to one of two universal forms on the time scale of its mean: either quasi-deterministic (delta-like) or quasi-memoryless (exponential). Building on the graph-theoretical interpretation of first-passage processes, here we provide a unifying explanation for these universal limits based on the distribution of the eigenvalues of the generator matrix. Then, we derive general conditions under which the distribution converges to either the deterministic or exponential limit. We demonstrate the theory by applying it to a generic birth-death process and conclude by discussing illustrative cases where the simple limiting behavior does not hold, which contradicts the naive expectation that a forward bias is sufficient to lead to a deterministic outcome.
Keywords: first-passage time; Markov chain; master equation; graph theory; large systems