Unverified50% confidenceFactExact time
Brenier's theorem (1991) states that when the source distribution is absolutely continuous, the unique optimal map transporting the source distribution to the target distribution under squared Euclidean cost must be the gradient of some convex function (the Brenier potential).
1
Sources
50%
Confidence
Long-term
Relevance
9/21/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe Berry-Esseen theorem provides an upper bound on the difference between the distribution function of a standardized sum and the standard normal distribution, where this upper bound is proportional to n^{-1/2} and proportional to the third absolute moment of the original distribution.63% similarUnverifiedCordero-Erausquin and Klartag proved the moment measure decomposition theorem in 2015: any probability measure ρ with a first moment, zero barycenter, and support not contained in a hyperplane can be decomposed into a specific form, where the transport map is the gradient of a convex function u.61% similarUnverified扩散模型的数学基础来源于物理学中的布朗运动和统计力学中的朗之万动力学，其代表作包括Stable Diffusion和DALL·E59% similarUnverifiedThe Poisson distribution was proposed by French mathematician Siméon Denis Poisson in 1838 and is a classic probability model describing the number of occurrences of low-frequency independent events per unit time.59% similarUnverifiedAnderson proved in 1982 that any forward diffusion process has a corresponding reverse SDE, whose drift term depends on the log-gradient of the data distribution (the score function).59% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/937737API
curl https://kongchang.com/api/v1/knowledge/claims/937737MCP
get_claim(id=937737)