Extreme-value statistics of stochastic transport processes

Guillet, Alexandre; Roldán, Édgar; Jülicher, Frank

doi:10.1088/1367-2630/abcf69

Cited by 16 publications

(16 citation statements)

References 89 publications

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“…is directly verified for any thresholds [33]. In addition, the mean dynamical activity is given by E[N τx ] = x coth( /2) and is in agreement with the KUR, [32].…”

Section: Applicationssupporting

confidence: 65%

Kinetic uncertainty relation on first-passage time for accumulated current

Hiura

Sasa

2021

Phys. Rev. E

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The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.

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“…is directly verified for any thresholds [33]. In addition, the mean dynamical activity is given by E[N τx ] = x coth( /2) and is in agreement with the KUR, [32].…”

Section: Applicationssupporting

confidence: 65%

Kinetic uncertainty relation on first-passage time for accumulated current

Hiura

Sasa

2021

Phys. Rev. E

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“…In this appendix, we derive the asymptotic behaviour of M n (t) for Brownian motion whose exact expression is given in Eq. (15). Below, we look at the behaviour of M n (t) for large and short times separately.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Extreme Value Statistics (EVS) sits on the heart of a branch of statistics which deals with the probabilities generated by random processes responsible for such unusual extreme events [1][2][3][4][5][6][7][8]. The study of EVS has been extremely important in the field of disordered systems [9,10], fluctuating interfaces [11,12], interacting spin systems [13], stochastic transport models [14,15], random matrices [16][17][18], ecology [19], in binary search trees [20] and related computer search algorithms [21,22] and even in material science [23]. We refer to these extensive reviews which provide detailed account of recent theoretical and application based progresses of EVS in science.…”

Section: Introductionmentioning

confidence: 99%

Extremal statistics for stochastic resetting systems

Singh,

Pal

2021

Preprint

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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.

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“…A study of these kinetic regimes is based on the theory of bifurcations and analysis of basins of attraction. It is well known that in dynamical models with strong nonlinearity even seemingly small random disturbances can complicate behaviour and cause stochastic transport [17][18][19] with various unexpected noise-induced effects [20][21][22][23][24][25][26][27][28][29]. Here, the phenomena of coherence and anti-coherence resonance attract attention of researchers [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

Bashkirtseva

Slepukhina

2022

Phil. Trans. R. Soc. A.

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Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

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Extreme-value statistics of stochastic transport processes

Cited by 16 publications

References 89 publications

Kinetic uncertainty relation on first-passage time for accumulated current

Kinetic uncertainty relation on first-passage time for accumulated current

Extremal statistics for stochastic resetting systems

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

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