Extremal statistics for stochastic resetting systems

Abstract

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

arXiv comment23 pages, 8 figures

References in corpus (85)

• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• First Passage Under Restart
• Universality Classes for Extreme Value Statistics
• First order transition for the optimal search time of Lévy flights with resetting
• Optimal stochastic restart renders fluctuations in first passage times universal
• Experimental realization of diffusion with stochastic resetting
• Diffusion under time-dependent resetting
• Run and tumble particle under resetting: a renewal approach
• Large Deviations of Extreme Eigenvalues of Random Matrices
• Diffusion in a potential landscape with stochastic resetting
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• Extreme value statistics of correlated random variables: a pedagogical review
• Stochastic resetting in backtrack recovery by RNA polymerases
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Diffusion with stochastic resetting at power-law times
• Exact Maximal Height Distribution of Fluctuating Interfaces
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• First passage under stochastic resetting in an interval
• Freezing and extreme value statistics in a Random Energy Model with logarithmically correlated potential
• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Boosting search by rare events
• Stochastic thermodynamics of resetting
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records
• Size effects in micro and nanoscale materials fracture
• Search with home returns provides advantage under high uncertainty
• Large deviations for Markov processes with resetting
• Restart could optimize the probability of success in a Bernoulli trial
• Resetting processes with non-instanteneous return
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Scaled Brownian motion with renewal resetting
• Work fluctuations and Jarzynski equality in stochastic resetting
• Quantum dynamics with stochastic reset
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Maximal Height Scaling of Kinetically Growing Surfaces
• Exact distribution of the maximal height of p vicious walkers
• Landau theory of restart transitions
• Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology
• Statistics at the tip of a branching random walk and the delay of traveling waves
• First passage under restart with branching
• Integral Fluctuation Theorems for Stochastic Resetting Systems
• Symmetric Exclusion Process under Stochastic Resetting
• Spatial extent of an outbreak in animal epidemics
• Stochastic resetting with stochastic returns using external trap
• Diffusion with stochastic resetting is invariant to return speed
• Ising model with stochastic resetting
• On the time to reach maximum for a variety of constrained Brownian motions
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Transport properties of random walks under stochastic non-instantaneous resetting
• Extreme Value Statistics and Traveling Fronts: An Application to Computer Science
• Generalized arcsine laws for fractional Brownian motion
• Active Brownian Motion in two-dimensions under Stochastic Resetting
• Invariants of motion with stochastic resetting and space-time coupled returns
• Stochastic resetting in underdamped Brownian motion
• Properties of additive functionals of Brownian motion with resetting
• Hitting probability for anomalous diffusion processes
• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks
• Traveling Waves, Front Selection, and Exact Nontrivial Exponents in a Random Fragmentation Problem
• Time to reach the maximum for a random acceleration process
• Condensation and Extreme Value Statistics
• Extremal statistics of curved growing interfaces in 1+1 dimensions
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Extreme-Value Statistics of Fractional Brownian Motion Bridges
• Local time of diffusion with stochastic resetting
• Space-dependent diffusion with stochastic resetting: A first-passage study
• Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries
• Mean perimeter and area of the convex hull of a planar Brownian motion in the presence of resetting
• Random acceleration process under stochastic resetting
• The longest excursion of stochastic processes in nonequilibrium systems
• Stochastic resetting on comb-like structures
• Multifractality and Freezing Phenomena in Random Energy Landscapes: an Introduction
• Time between the maximum and the minimum of a stochastic process
• Distribution of the Time Between Maximum and Minimum of Random Walks
• Extremal Properties of Random Systems
• Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time
• Traveling Front Solutions to Directed Diffusion Limited Aggregation, Digital Search Trees and the Lempel-Ziv Data Compression Algorithm
• Exact extreme value statistics at mixed order transitions
• Mitigating long transient time in deterministic systems by resetting
• Stochastic resetting antiviral therapies prevents drug resistance development
• Extreme value theory for constrained physical systems
• Real-space Condensation in Stochastic Mass Transport Models
• Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports

Cited by in corpus (30)

• The inspection paradox in stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• First-passage Brownian functionals with stochastic resetting
• Number of distinct sites visited by a resetting random walker
• Extreme value statistics and arcsine laws for heterogeneous diffusion processes
• Mitigating long queues and waiting times with service resetting
• Universal framework for record ages under restart
• Time to reach the maximum for a stationary stochastic process
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Random walks on complex networks under time-dependent stochastic resetting
• Maximum and records of random walks with stochastic resetting
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Effect of stochastic resetting on Brownian motion with stochastic diffusion coefficient
• Extreme Value Statistics and Arcsine Laws of Brownian Motion in the Presence of a Permeable Barrier
• Extremal statistics for a resetting Brownian motion before its first-passage time
• Entropy rate of random walks on complex networks under stochastic resetting
• Optimal conditions for first passage of jump processes with resetting
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Efficiency of a microscopic heat engine subjected to stochastic resetting
• Generalized arcsine laws for a sluggish random walker with subdiffusive growth
• Emerging cost-time Pareto front for diffusion with stochastic return
• Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes
• Exact joint distributions of three global characteristic times for Brownian motion
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Full Record Statistics of 1d Random Walks
• The distribution of the maximum of independent resetting Brownian motions
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Stationary state of harmonic chains driven by boundary resetting
• Short-time large deviations of first-passage functionals for high-order stochastic processes