scholarly journals Gromov’s Waist of Non-radial Gaussian Measures and Radial Non-Gaussian Measures

2020 ◽  
pp. 1-27
Author(s):  
Arseniy Akopyan ◽  
Roman Karasev
Keyword(s):  
Gaussian Measures ◽  
Non Gaussian

DIFFUSION PROCESSES ON PATH SPACES WITH INTERACTIONS

2001 ◽  
Vol 13 (02) ◽  
pp. 199-220 ◽  
Author(s):  
YUU HARIYA ◽  
HIROFUMI OSADA
Keyword(s):  
Diffusion Processes ◽  
Gibbs Measures ◽  
Infinite Volume ◽  
Gaussian Measures ◽  
Uhlenbeck Process ◽  
Mild Conditions ◽  
Carré Du Champ ◽  
Form Theory ◽  
The One ◽  
Non Gaussian

We construct dynamics on path spaces C (ℝ; ℝ) and C([-r, r];ℝ) whose equilibrium states are Gibbs measures with free potential φ and interaction potential ψ. We do this by using the Dirichlet form theory under very mild conditions on the regularity of potentials. We take the carré du champ similar to the one of the Ornstein–Uhlenbeck process on C([0, ∞);ℝ). Our dynamics are non-Gaussian because we take Gibbs measures as reference measures. Typical examples of free potentials are double-well potentials and interaction potentials are convex functions. In this case the associated infinite-volume Gibbs measures are singular to any Gaussian measures on C(ℝ;ℝ).

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