Brownian motion on Perelman’s almost Ricci-flat manifold
Brownian motion on Perelman’s almost Ricci-flat manifold
Abstract We study Brownian motion and stochastic parallel transport on Perelman’s almost Ricci flat manifold <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>ℳ</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mi>M</m:mi> <m:mo>×</m:mo> <m:msup> <m:mi>𝕊</m:mi> <m:mi>N</m:mi> </m:msup> <m:mo>×</m:mo> <m:mi>I</m:mi> </m:mrow> </m:mrow> </m:math> {\mathcal{M}=M\times\mathbb{S}^{N}\times I} , whose dimension depends on a parameter N unbounded from above. We construct sequences of projected …