The average shape of a fluctuation: universality in excursions of stochastic processes
arXiv:cond-mat/0301068 · doi:10.1103/PhysRevLett.90.060601
Abstract
We study the average shape of a fluctuation of a time series x(t), that is the average value <x(t)-x(0)>_T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form <x(t) - x(0)>_T = T^αf(t/T) is obeyed. The scaling function f(s) is to a large extent independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.
arXiv comment5 pages, 5 figures, accepted for publication in Phys. Rev. Lett
References in corpus (6)
- Crackling Noise
- Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
- Noise in disordered systems: The power spectrum and dynamic exponents in avalanche models
- Universal Pulse Shape Scaling Function and Exponents: A Critical Test for Avalanche Models applied to Barkhausen Noise
- On the power spectrum of magnetization noise
- Inelastic collapse of a randomly forced particle
Cited by in corpus (32)
- Criticality in the brain: A synthesis of neurobiology, models and cognition
- Bulk Metallic Glasses Deform via Slip Avalanches
- Beyond power laws: Universality in the average avalanche shape
- Power-law statistics and universal scaling in the absence of criticality
- Signature of effective mass in crackling noise asymmetry
- Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
- Self-Organized Bistability Associated With First-Order Phase Transitions
- A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
- Time-series thresholding and the definition of avalanche size
- Temporal profiles of avalanches on networks
- Brownian motion: a paradigm of soft matter and biological physics
- Bursts of Active Transport in Living Cells
- Theoretical foundations of studying criticality in the brain
- Temporal and spacial evolution of bursts in creep rupture
- Asymmetric damage avalanche shape in quasi-brittle materials and sub-avalanches (aftershocks) clusters
- Average trajectory of returning walks
- Shape of a Barkhausen pulse
- Field-theoretic approach to the universality of branching processes
- How we move is universal: scaling in the average shape of human activity
- How ants move: individual and collective scaling properties
- Classes of critical avalanche dynamics in complex networks
- Avalanche dynamics in higher dimensional fiber bundle models
- Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
- Complexity emerges in measures of the marking dynamics in football games
- Universal Excursion and Bridge shapes in ABBM/CIR/Bessel processes
- Mechanisms of evolution of avalanches in regular graphs
- First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect
- Residence Time Near an Absorbing Set
- Finite-size scaling of critical avalanches
- Analytical Methods and Field Theory for Disordered Systems
- From Markovian to non-Markovian persistence exponents
- Average shape of fluctuations for subdiffusive walks