TY - JOUR
T1 - Convexity of the support of the displacement interpolation
T2 - Counterexamples
AU - Santambrogio, Filippo
AU - Wang, Xu Jia
N1 - Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - Given two smooth and positive densities ρ0,ρ1 on two compact convex sets K0,K1, respectively, we consider the question whether the support of the measure ρt obtained as the geodesic interpolant of ρ0 and ρ1 in the Wasserstein space W2(Rd) is necessarily convex or not. We prove that this is not the case, even when ρ0 and ρ1 are uniform measures.
AB - Given two smooth and positive densities ρ0,ρ1 on two compact convex sets K0,K1, respectively, we consider the question whether the support of the measure ρt obtained as the geodesic interpolant of ρ0 and ρ1 in the Wasserstein space W2(Rd) is necessarily convex or not. We prove that this is not the case, even when ρ0 and ρ1 are uniform measures.
KW - Displacement convexity
KW - Log-concave distributions
KW - Optimal transport
UR - http://www.scopus.com/inward/record.url?scp=84961839604&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2016.02.016
DO - 10.1016/j.aml.2016.02.016
M3 - Article
SN - 0893-9659
VL - 58
SP - 152
EP - 158
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
ER -