On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations

TY - UNPB

T1 - On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations

AU - Baudoin, Fabrice

AU - Kuijper, Teije

N1 - v2: Minor edits

PY - 2024/10/9

Y1 - 2024/10/9

N2 - We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from which one point has been removed; the odd dimensional spheres from which a great hypersphere has been removed; and the complex anti-de Sitter spaces. Our analysis is based on the geometry of the Hopf and anti-de Sitter fibrations, and on the relationship between winding and area forms.

AB - We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from which one point has been removed; the odd dimensional spheres from which a great hypersphere has been removed; and the complex anti-de Sitter spaces. Our analysis is based on the geometry of the Hopf and anti-de Sitter fibrations, and on the relationship between winding and area forms.

KW - math.PR

KW - math.DG

M3 - Preprint

BT - On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations

ER -