Related papers: On the nodal structures of random fields -- a deca…

In this paper we provide an overview of important research works on response-adaptive randomization completed in the past decades.

In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…

Experimental results on hadronic structures are discussed in view of our physics understanding. Achievements and challenges are noted.

This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…

In this article we try to give a condensed panoramic view of the development of two-dimensional rational conformal field theory in the last twenty-five years.

This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…

We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential…

In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…

Random fields have remained a topic of great interest over past decades for the purpose of structured inference, especially for problems such as image segmentation. The local nodal interactions commonly used in such models often suffer the…

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

The way a field transforms under rotations determines its statistics--as is easy to see for scalar, Dirac, and vector fields.

In the past, different works based on numerical simulations have been presented to explain magnetic fields (MFs) in the large scale structure and within galaxy clusters. In this review, I will summarize the main findings obtained by…

We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.

Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important…

This work contains a set of lectures on defect structures, mainly in models described by scalar fields in diverse dimensions.

In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders.

In this paper we investigate the properties of nodal structures in random wave fields, and in particular we scrutinize their recently proposed connection with short-range percolation models. We propose a measure which shows the difference…

The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…