Extremal statistics for stochastic resetting systems

While averages and typical fluctuations often play a major role in understanding the behavior of nonequilibrium system, this nonetheless is not always true. Rare events large are also pivotal when thorough analysis system being done. In context, statistics extreme contrast to average plays an important role, as has been discussed fields ranging from statistical mathematical physics climate, finance, ecology. Herein, we study value (EVS) stochastic resetting systems, which have recently gained significant interest due its ubiquitous enriching applications physics, chemistry, queuing theory, search processes, computer science. We present detailed for finite time extremals (maximum arg-maximum, i.e., maximum reached) spatial displacement such system. particular, derive exact renewal formula that relates joint distribution arg-maximum reset process measures underlying process. Benchmarking our results trajectory pertain Gumbel class sample size, show density attains uniform independent at observation time. This emerges manifestation property mechanism. The augmented with wide spectrum Markov non-Markov processes under resetting, namely, simple diffusion, diffusion drift, Ornstein-Uhlenbeck process, random acceleration one dimension. Rigorous presented first two setups, while latter supported heuristic numerical analysis.