Geodesic
Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle
Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 109-118

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

Via elements of second order differential geometry on smooth Wasserstein spaces of probability measures we give an explicit formula for a Laplacian in the case that the Wasserstein space is based on the unit circle. The Laplacian on this infinite dimensional manifold is calculated as trace of the Hessian in the sense of Zeta function regularization. Its square field operator is the square norm of the Wasserstein gradient.
Keywords: Wasserstein distance, smooth Wasserstein space, smooth Lie bracket, entropy, Riemann zeta-function.
Mots-clés : optimal transport 
@article{THSP_2011_17_1_a11,
     author = {Christian Selinger},
     title = {Zeta function regularized {Laplacian} on the smooth {Wasserstein} space above the unit circle},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {109--118},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a11/}
}
TY  - JOUR
AU  - Christian Selinger
TI  - Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle
JO  - Teoriâ slučajnyh processov
PY  - 2011
SP  - 109
EP  - 118
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a11/
LA  - en
ID  - THSP_2011_17_1_a11
ER  - 
%0 Journal Article
%A Christian Selinger
%T Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle
%J Teoriâ slučajnyh processov
%D 2011
%P 109-118
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a11/
%G en
%F THSP_2011_17_1_a11
Christian Selinger. Zeta function regularized Laplacian on the smooth Wasserstein space above the unit circle. Teoriâ slučajnyh processov, Tome 17 (2011) no. 1, pp. 109-118. http://geodesic.mathdoc.fr/item/THSP_2011_17_1_a11/