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We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…
In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed…
A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…
The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling…
This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…
We introduce an equivariant version of the weak expectation property (WEP) at the level of operator modules over completely contractive Banach algebras $A$. We prove a number of general results---for example, a characterization of the…
Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in combinatorial dynamics. The new construction of the index in…
Based on a weak convergence argument, we provide a necessary and sufficient condition that guarantees that a nonnegative local martingale is indeed a martingale. Typically, conditions of this sort are expressed in terms of integrability…
In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization are necessary and can be applied to scenarios involving…
In this paper, we introduce the notions uniformly p-convergent sets and weakly p-sequentially continuous differentiable mappings. Then we obtain a sufficient condition for those Banach spaces which either contain no copy of $\ell_1$ or have…
In this work we present different results concerning mixing properties of multivariate infinitely divisible (ID) stationary random fields. First, we derive some necessary and sufficient conditions for mixing of stationary ID multivariate…
We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…
In this article, we consider minimal $L^2$ integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and…
We show that a coded system is mixing if and only if it is totally transitive and if in addition it has a relatively prime generator, then it has strong property P. We continue by showing that a mixing half-synchronized system has such a…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
In the present paper, we define the concept of weak topological conjugacy and we establish sufficient conditions to obtain this kind of topological conjugacy between two limit sets. We use the character of recurrence to obtain the results.
This work extends the idea of matched pairs presented by Majid in \cite{Majid} and Takeuchi in \cite{Takeuchi} for the context of weak bialgebras and weak Hopf algebras. We introduce, also inspired by partial matched pairs…
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…
Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown to coincide with the unique strong solution determined by the same initial condition on the maximal existence interval of the latter. The…