We study a one-parameter family of discrete-time quantum walk models on $\mathbb{Z}$ and ${\mathbb{Z}}^2$ associated with the Hadamard walk. Weak convergence in the long-time limit of all moments of the walker's pseudovelocity on $\mathbb{Z}$ and ${\mathbb{Z}}^2$ is proved. Symmetrization on $\mathbb{Z}$ and ${\mathbb{Z}}^2$ is theoretically investigated, leading to the resolution of the Konno-Namiki-Soshi conjecture in the special case of symmetrization of the unbiased Hadamard walk on $\mathbb{Z}$. A necessary condition for the existence of a phenomenon known as localization is given. DOI: http://dx.doi.org/10.1103/PhysRevA.84.012324 ©2011 American Physical Society

In this paper, we propose a useful method without adding any extra parameters to obtain new probability distributions. The proposed family is a combination of the two existing families of distributions and is called a weighted sine-G family. A two-parameter special member of the weighted sine-G family, using the Weibull distribution as a baseline model, is considered and investigated in detail. Some distributional properties of the weighted sine-G family are derived. Different estimation methods are considered to estimate the parameters of the special model of the weighted sine-G family. Furthermore, simulation studies based on these different methods are also provided. Finally, the applicability and usefulness of the weighted sine-G family are demonstrated by analyzing two data sets taken from the engineering sector.

In this paper the return probability of the one-dimensional discrete-time quantum walk is studied. We derive probabilistic formulas for the return probability related to the quantum walk governed by the Fibonacci coin.

In this article, we introduce a new class of distributions called the New Exponentiated T-X family of distributions. A special sub-model of the proposed family, called a new exponentiated exponential-Weibull is considered in detail. Some structural properties associated with this new class of distributions are obtained. Certain characterizations of the proposed family are presented. Maximum likelihood estimators of the model parameters are obtained and Monte Carlo simulation study is conducted to evaluate the performances of these estimators. Finally, the importance of the new family is illustrated empirically via a real-life application.

In this paper we present an introduction to the theory of anyons and discuss how basis sets and matrix representation of the interaction terms can be obtained, using non-Abelian Fibonacci anyons. We show that the change of basis matrix for certain fusion trees called pentagons is given by a certain unitary matrix which is introduced in Sec. I, and denoted F$\tau${}$\tau${},$\tau${},$\tau${} throughout the remainder of the paper. We perform a quantum walk with the Fibonacci anyons governed by the unitary matrix F$\tau${}$\tau${},$\tau${},$\tau${} and obtain the limiting distribution of the walk.