Universal cutoff for Dyson Ornstein Uhlenbeck process

Boursier, Jeanne; Chafäı, Djalil; Labbé, Cyril

doi:10.1007/s00440-022-01158-5

Cited by 5 publications

(4 citation statements)

References 46 publications

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“…By (1.6) we have that G * , G * are monotonic decreasing. We note that (1.6) is natural in the context of homogeneous Markov processes and holds true for various distances/discrepancies of interest, see for instance Lemma B.3 (Monotonicity) in [26]. Under (1.6) one can see that (iii) implies (ii).…”

Section: Introductionmentioning

confidence: 85%

“…For more general Markov processes taking values in continuous state-spaces there are relatively few results showing the asymptotic cut-off phenomenon. They include linear SDEs driven by Brownian motion and more general Lévy perturbations [8,18,9,17,20,51], non-linear over-damped and under-damped Langevin dynamics driven by Brownian motion and more general Lévy perturbations [15,16,12,6,10,55], linear heat and wave SPDEs driven by Lévy noise [14], multivariate geometric Brownian motion [11], Dyson-Ornstein-Uhlenbeck process [26], the biased adjacent walk on the simplex [50], Brownian motion on families of compact Riemannian manifolds [62]. Recently, the asymptotic cut-off has been studied in: coagulation-fragmentation systems [65], machine learning for neural networks [4], quantum Markov chains [46], open quadratic fermionic systems [76], chemical kinetics [22], viscous energy shell model [13], and random quantum circuits [67].…”

Section: Introductionmentioning

confidence: 99%

“…The model (1.1) is introduced in 1985 by J. Cox, J. Ingersoll and S. Ross to describe the evolution of instantaneous interest rate at time t, X ε t (x), with mean reversion of the interest rate towards the long-term value b/a with the speed of adjustment a. Nowadays, it is known as a Cox-Ingersoll-Ross (CIR) process, see [29]. In Section 1.5 in [26] it is shown that cut-off phenomenon holds true, as the number of sampling increases, for a particular CIR model (Bessel process), which can be written as a square of an Ornstein-Uhlenbeck process. Furthermore, singular SDEs of the type (1.1) emerge in the model of evolution of chemical reactions and population dynamics as diffusion approximations of res-caled Markov jump processes, see for instance [5,35,70] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes

Barrera¹,

Pardo²

2020

Electron. J. Probab.

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In this paper, we study the cut-off phenomenon of d-dimensional Ornstein-Uhlenbeck processes which are driven by Lévy processes under the total variation distance. To be more precise, we prove the abrupt convergence under the total variation distance of the aforementioned process to its equilibrium. Despite that the invariant distribution is not explicit, its distributional properties allow us to deduce that a profile function always exists in the reversible cases and it may exist in the non-reversible cases. The cut-off phenomenon for the average and superposition processes is also determined.

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes

Barrera¹,

Pardo²

2020

Electron. J. Probab.

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“…is non-increasing, see Lemma B.3 (Monotonicity) in [31]. In order to infer no cutoff we combine (6.1) with the following estimate, which is a direct consequence of Theorem 3.1.…”

mentioning

confidence: 99%

Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise

Barrera¹,

Högele²,

Pardo³

et al. 2023

Preprint

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This article establishes non-asymptotic ergodic bounds in the renormalized, weighted Kantorovich-Wasserstein-Rubinstein distance for a viscous energy shell lattice model of turbulence with random energy injection. The obtained bounds turn out to be asymptotically sharp and establish abrupt thermalization. The types of noise under consideration are Gaussian and symmetric α-stable, white and stationary Ornstein-Uhlenbeck noise, respectively, as well as general Lévy noise with second moments. Furthermore we establish the absence of abrupt thermalization in the inviscid limit case.

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Coercive inequalities on Carnot groups: taming singularities

Bou Dagher,

Zegarliński

2024

Anal.Math.Phys.

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In the setting of Carnot groups, we propose an approach of taming singularities to get coercive inequalities. To this end, we develop a technique to introduce natural singularities in the energy function U in order to force one of the coercivity conditions. In particular, we explore explicit constructions of probability measures on Carnot groups which secure Poincaré and even Logarithmic Sobolev inequalities. As applications, we get analogues of the Dyson–Ornstein–Uhlenbeck model on the Heisenberg group and obtain results on the discreteness of the spectrum of related Markov generators.

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Universal cutoff for Dyson Ornstein Uhlenbeck process

Cited by 5 publications

References 46 publications

Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes

Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes

Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise

Coercive inequalities on Carnot groups: taming singularities

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