Several Limit Theorems on Fuzzy Quantum Space

Limit theorems for quantum entropies

Compactification on soft fuzzy limit space

In this paper the concept of soft fuzzy filter on X, soft fuzzy prime filter on X, soft fuzzy ultrafilter on X, soft fuzzy minimal prime filter collections are introduced. The concept of soft fuzzy limit space (X, ltτ ) and the related properties are discussed. The functor ι from the collection of soft fuzzy filters F(X) to the collection of filters on X and the functor ω defined from the colle...

Almost sure central limit theorems on the Wiener space

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian elds. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.

Quantitative stable limit theorems on the Wiener space

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39–64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460–3505], and pr...

Limit theorems for discrete-time quantum walks on trees

We consider a discrete-time quantum walk Wt given by the Grover transformation on the Cayley tree. We reduce Wt to a quantum walk Xt on a half line with a wall at the origin. This paper presents two types of limit theorems for Xt. The first one is Xt as t → ∞, which corresponds to a localization in the case of an initial qubit state. The second one is Xt/t as t → ∞, whose limit density is given...