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Galton-Watson trees with vanishing martingale limit
Conditioning principle large deviations micro-canonical distribution sharp thresholds branching entropic repulsion
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2012/4/16
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, agrees up to generation $K$ with a regular $\mu$-ary tree, where $\mu$ is the essential mini...
The vanishing of L2 harmonic one-forms on based path spaces
L2 cohomology Hodge decomposition L2 harmonic forms path space Banach manifold Wiener measure
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2012/4/17
We prove the triviality of the first L2 cohomology class of based path spaces of Riemannian manifolds furnished with Brownian motion measure, and the consequent vanishing of L2 harmonic one-forms. We ...