Cover of: Random fields on the sphere | Domenico Marinucci

Random fields on the sphere

representation, limit theorems, and cosmological applications
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Cambridge University Press , Cambridge, New York
Statistical methods, MATHEMATICS / Probability & Statistics / General, Random fields, Spherical harmonics, Compact groups, Cosm
StatementDomenico Marinucci, Giovanni Peccati
SeriesLondon Mathematical Society lecture note series -- 389
ContributionsPeccati, Giovanni, 1975-
Classifications
LC ClassificationsQA406 .M37 2011
The Physical Object
Paginationp. cm.
ID Numbers
Open LibraryOL24917893M
ISBN 139780521175616
LC Control Number2011023821

Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields. The main emphasis is on tools from harmonic analysis, beginning with the representation theory for the group of rotations SO(3).

Many recent developments on the method of moments and cumulants for the analysis of Gaussian subordinated fields are Cited by: Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields.

The main emphasis is on tools from harmonic analysis, beginning with the representation theory for the group of rotations SO(3).Author: Domenico Marinucci, Giovanni Peccati. - Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications Domenico Marinucci and Giovanni Peccati Index More information.

Index High-resolution asymptotics, Homogeneous space, 18 Homomorphism, 16 Random fields on the sphere book of, 16 Hypercontractivity, Get this from a library.

Description Random fields on the sphere PDF

Random fields on the sphere: representation, limit theorems, and cosmological applications. [Domenico Marinucci; Giovanni Peccati] -- "Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields.

The main emphasis is on tools from harmonic analysis, beginning with the representation theory for. Get this from a library. Random fields on the sphere: representation, limit theorems and cosmological applications.

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[Domenico Marinucci; Giovanni Peccati] -- "Random Fields on the Sphere presents a comprehensive analysis of isotropic spherical random fields. The main emphasis is on tools from harmonic analysis, beginning with the representation theory for. We discuss also the spatio-temporal case, of sphere cross line.

In the continuous case, we investigate the link between the smoothness of paths and the decay rate of the angular power spectrum, following Tauberian work of the first author, Malyarenko, and Lang and Schwab.

Title: Random Fields on the Sphere Author: domenico marinucci & giovanni peccati Created Date: 8/25/ PM. Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Loève expansions with respect to the spherical harmonic functions and the angular power spectrum.

The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample Hölder continuity and sample differentiability of the random fields is discussed.

Rates of. This edition of The Sphere Handbook is the result of the most diverse and far-reaching consultation process in the history of Sphere.

Nearly 4, online comments were received from organisations, and more than 1, people participated in 60 in-person events hosted by partners in 40 countries. Sphere is a novel by Michael Crichton, his sixth novel under his own name and his sixteenth was adapted into the film Sphere in The story follows Norman Johnson, a psychologist engaged by the United States Navy, who joins a team of scientists assembled to examine a spacecraft of unknown origin discovered on the bottom of the Pacific Ocean.

Sphere, Michael Crichton Sphere is a novel by Michael Crichton. It was adapted into the film Sphere in The story follows Norman Johnson, a psychologist engaged by the United States Navy, who joins a team of scientists assembled to examine a spacecraft of unknown origin, discovered on the bottom of the Pacific Ocean/5(K).

To generate a random point on the sphere, it is necessary only to generate two random numbers, z between -R and R, phi between 0 and 2 pi, each with a uniform distribution To find the latitude (theta) of this point, note that z=Rsin(theta), so theta=sin -1 (z/R); its longitude is (surprise!) phi.

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined.

The Sphere Project – or ‘Sphere’ – was initiated in by a group of humanitarian non-governmental organisations (NGOs) and the International Red Cross and Red Crescent Movement. Their aim was to improve the quality of their actions during disaster response and to be held accountable for them.

They based Sphere’s. What is this book about. High-dimensional probability is an area of probability theory that studies random objects in Rn where the dimension ncan be very large. This book places par-ticular emphasis on random vectors, random matrices, and random projections. It teaches basic theoretical skills for the analysis of these objects, which include.

A sphere with radius 1 occupies a volume of (4/3)*π, which is about A cube whose sides touch this sphere has each side of length 2, to give a volume of 8.

The probability of a point chosen from a uniform random distribution in the cube being outside the sphere is. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust Cited by: tangobook On regression analysis of a certain random field on the unit sphere.

Extrema of rescaled locally stationary Gaussian fields on manifolds Qiao, Wanli and Polonik, Wolfgang, Bernoulli, ; The mean Euler characteristic and excursion probability of Gaussian random fields with stationary increments Cheng, Dan and Xiao, Yimin, Annals of Applied Probability, ; A central limit theorem for the Euler characteristic of a Gaussian excursion set Estrade, Anne and.

Early in the book, Adler & Taylor present Talagrand's condition for almost-sure continuity of random fields, as well as the Borel-TIS concentration inequality.

For such a clear presentation of this background material alone, the book is worth its weight in gold. The real content of the book is the recent s: 3. Series expansions of isotropic Gaussian random fields on $\\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed.

Such representations provide an alternative to the standard Karhunen-Loève expansions of isotropic random fields in terms of spherical harmonics.

Their multilevel localized structure of basis functions is especially useful in. Next, normalize each random vector to have unit norm so that the vector retains its direction but is extended to the sphere of unit radius.

As each vector within the region has a random direction, these points will be uniformly distributed on a sphere of radius 1. Discover 'The Sphere' in New York, New York: This sculpture by artist Fritz Keonig survived the 9/11 attacks and now stands as a monument to the victims.

Choose a, b, c to be three random numbers each between -1 and 1. Calculate r2 = a^2 + b^2 + c^2. If r2 > (=the point isn't in the sphere) or r2 sphere) you discard the values, and pick another set of random a, b, c. have written this book to cover the theory likely to be useful in the next 40 years, just as automata theory, algorithms and related topics gave students an advantage in the last 40 years.

My research interests lie in computational mathematics, statistics, machine learning, and data science.

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In particular, I am working on deep learning, graph neural networks, applied harmonic analysis, Bayesian inference, information geometry, random fields, and applications to healthcare, biomedical technology and. This method can be applied to the sphere in any number of dimensions, as illustrated below for the cases D = 1, 2, As you might have already noticed, the problem with this sampling algorithm is that the region in which the points are sampled (the cube) and the region where they are accepted (the sphere) rapidly grow more distinct from each other as we go to higher dimensions.

This is problem A-6 from the Putnam mathematical Competition. Solutions have been published in American Mathematical Monthly (vn 8, ) by the.

Killing fields on a 2-sphere. The Killing fields on the two-sphere, or any sphere, should be, in a sense, "obvious" from ordinary intuition: spheres, being sphere-symmetric, should posses Killing fields that are generated by infinitessimal rotations about any axis.

This is. Net work done by the field in carrying a test charge over a closed loop is zero because the field inside the conductor is zero.

Hence, electric field is zero, whatever is the shape. Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another.

Charge on a conductor would be free to move and would end up on the surface. This charge density is uniform throughout the sphere. Charge Q is uniformly distributed throughout a sphere of radius a. Find the electric field at a radius r. First consider r > a; that is, find the electric field at a point outside the sphere.

p-norm is used to measure the distance between sequential iterations of the mapping f on the Riemann sphere Discrete Lagrangian Descriptor = DLD The simple idea is to compute the p-norm version of Lagrangian descriptors, not for the points on the complex plane, but for their projections on the Riemann sphere in the extended complex plane.Suppose you write a random variable that generates the identity mapping with probability $1/42$, and wraps the sphere one time around itself with probability $1 - 1/42$.

Then you "investigate" how often the mapping is homotopically trivial.Use the fact that if you cut a sphere of a given radius with two parallel planes, the area of the strip of spherical surface between the planes depends only on the distance between the planes, not on where they cut the sphere.

Thus, you can get a uniform distribution on the surface using two uniformly distributed random variables.