3e Some integral geometry............... 36

نویسنده

  • J. E. Taylor
چکیده

3a An instructive toy model: two paradoxes We start with a very simple random trigonometric polynomial (even simpler than 1c12): (3a1) X(t) = ζ cos t+ η sin t where ζ, η are independent N(0, 1) random variables. Its distribution is the image of γ under the map (x, y) 7→ (t 7→ x cos t+ y sin t). Time shifts of the trigonometric polynomial correspond to rotations of R, (3a2) X(t− α) = ζ(cos t cosα + sin t sinα) + η(sin t cosα− cos t sinα) = = (ζ cosα− η sinα) cos t+ (ζ sinα + η cosα) sin t ; the process (3a1) is stationary, that is, invariant under time shifts; (3a3) EX(t) = 0 , EX(s)X(t) = cos(s− t) . The random variable (3a4) M = max t∈R |X(t)| = √

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

متن کامل

Solution of Dirac's equation in Reissner-Nordström geometry.

The nature of the singularity at the origin of the solution of Dirac's equation in Reissner-Nordström geometry is different from that in flat space. Here, both independent solutions are regular at the origin, and both give a convergent normalization integral. The choice between the two solutions is made by requiring that the variational integral, from which the differential equation can be deri...

متن کامل

Institute for Mathematical Physics Intermediate Inversion Formulas in Integral Geometry Intermediate Inversion Formulas in Integral Geometry

We solve the following \intermediate" problem of integral geometry: to reconstruct integrals of a function over p-dimensional planes in R n starting from its integrals over k-planes, where p < k. Some generalizations are also presented.

متن کامل

Quantization of linear algebra and its application to integral geometry

In order to construct good generating systems of two-sided ideals in the universal enveloping algebra of a complex reductive Lie algebra, we quantize some notions of linear algebra, such as minors, elementary divisors, and minimal polynomials. The resulting systems are applied to the integral geometry on various homogeneous spaces of related real Lie groups.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006