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We study convergence to stationarity for random walks on dynamic random digraphs with given degree sequences. The digraphs undergo full regeneration at independent geometrically distributed random time intervals with parameter $\alpha$.…
On a measure theoretical dynamical system with spectral gap property we consider non-integrable observables with regularly varying tails and fulfilling a mild mixing condition. We show that the normed trimmed sum process of these…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
This article addresses mixing and diffusion properties of passive scalars advected by rough ($C^\alpha$) shear flows. We show that in general, one cannot expect a rough shear flow to increase the rate of inviscid mixing to more than that of…
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…
The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the…
We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one…
The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random…
We give sufficient conditions ensuring that a $\psi$-mixing property holds for the sequence of empirical CDFs associated to a conjugate process.
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
Mixing of materials is fundamental to many natural phenomena and engineering applications. The presence of discontinuous deformations - such as shear banding or wall slip - creates new mechanisms for mixing and transport beyond those…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…
We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and…
De Finetti's theorem, also called the de Finetti-Hewitt-Savage theorem, is a foundational result in probability and statistics. Roughly, it says that an infinite sequence of exchangeable random variables can always be written as a mixture…
Mixing of finite time-homogeneous Markov chains is well understood nowadays, with a rich set of techniques to estimate their mixing time. In this paper, we study the mixing time of random walks in dynamic random environments. To that end,…
We study mixed multiquadratic field extensions as splitting fields for central simple algebras of exponent $2$ in characteristic $2$. As an application, we provide examples of nonexcellent mixed biquadratic field extensions.
In this paper, we investigate the law of large numbers for strictly stationary random fields, that is, we provide sufficient conditions on the moments and the dependence of the random field in order to guarantee the almost sure convergence…
In this short note we provide an elementary proof that a certain type of nonuniform sequential Doeblin minorization condition implies non-uniform sequential "geometric" ergodicity. Using this result several limit theorems for inhomogeneous…
We consider suspension flows built over interval exchange transformations with the help of roof functions having an asymmetric logarithmic singularity. We prove that such flows are strongly mixing for a full measure set of interval exchange…