CANCELLED: Long-range dependent processes: confinement & heterogeneity

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• Ralf Metzler (Universität Potsdam)
• Monday 06 November 2023, 10:00-11:00
• Seminar Room 1, Newton Institute.

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Stochastic processes driven by Gaussian yet power-law correlated noise, such as Mandelbrot’s fractional Brownian motion (FBM) represent a quite ubiquitous, effective description of the dynamics in a range of complex systems, e.g., for the motion of tracers in viscoelastic environments, in “rough” financial data, or for the persistent motion of animals. FBM is an ergodic yet strongly non-Markovian process, with often surprising behavior. In this talk I will briefly introduce these processes and demonstrate that in strong confinement their probability density may assume non-Boltzmannian, multimodal stationary shapes, while in soft external potentials no steady state exists. An application of this effect to brain fibre growth is discussed. In heterogeneous environments the memory correlations of a diffusing test particle may become a (random or deterministic) function of time or space. For these cases I will introduce “doubly-stochastic” extensions such as FBM with random scaling exponent, memory-multimodal FBM , and FBM with a “diffusing diffusivity”. Finally I will address long-range dependent processes in the case when the memory (Hurst) exponent and the noise strength become explicit functions of time, e.g., in a membrane subject to temperature variations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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