Geodesic
The variance of the number of windings of the random field along the planar curve
Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 33-53.

Voir la notice de l'article provenant de la source Math-Net.Ru

This article is devoted to the study of the distribution of a winding number of a random vector field along the fixed plane curve. For some case of Gaussian homogeneous isotropic vector field, an explicit expression for the variance of the number of windings along the planar curve is given.
Keywords: Random field, isotropic random field, windings of vector field. 
@article{THSP_2012_18_2_a4,
     author = {V. A. Kuznetsov},
     title = {The variance of the number of windings of the random field along the planar curve},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {33--53},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a4/}
}
TY  - JOUR
AU  - V. A. Kuznetsov
TI  - The variance of the number of windings of the random field along the planar curve
JO  - Teoriâ slučajnyh processov
PY  - 2012
SP  - 33
EP  - 53
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a4/
LA  - en
ID  - THSP_2012_18_2_a4
ER  - 
%0 Journal Article
%A V. A. Kuznetsov
%T The variance of the number of windings of the random field along the planar curve
%J Teoriâ slučajnyh processov
%D 2012
%P 33-53
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a4/
%G en
%F THSP_2012_18_2_a4
V. A. Kuznetsov. The variance of the number of windings of the random field along the planar curve. Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 33-53. http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a4/

[1] R. J. Adler, J. E. Taylor, Random Fields and Geometry, Springer, New York, 2007 | MR | Zbl

[2] M. A. Krasnosel'skii, A. I. Perov, A. I. Povolockii, P. P. Zabreiko, Plane Vector Fields, Academic Press, New York, 1966 | MR

[3] Craig L. Zirbel, Wojbor A. Woyczyński, “Rotation of particles in polarized Brownian flows”, Stochast. and Dynamics, 2:1 (2002), 109–129 | DOI | MR | Zbl

[4] G. B. Arfken, H. J. Weber, F. E. Harris, Mathematical Methods for Physicists, Academic Press, New York, 2012