7 problems

Convergence-rate conjecture. Theorem … and $$ increase with $\alpha$.

Let $D\subset\mathbb R^d$ be open, bounded, and convex, and let $\mathcal W$ be a renormalization class on $\overline D$. Assume that the asymptotic fixed-point equation has a uniq…

Let $D\subset\mathbb R^d$ be the domain of a renormalization class $\mathcal W$, let $(c_k)_{k\geq0}$ be positive migration constants, and define $s_n=\sum_{k=0}^{n-1}c_k^{-1}$ and…

Let $b1 b2$ and $d_m$ satisfy … and … Here $b1$ is the volume growth exponent, $b2$ is the escape time exponent, and $d_m$ is the martingale dimension, also called the martingale i…

A sub-Riemannian diffusion killed when it exits a sufficiently small metric ball is expected to exhibit an analogous small-ball spectral convergence to the corresponding nilpotent…

Let $\mathcal{A}$ be a manifold in $\mathbb{R}^d$ without boundary, and let $(X_t,\eta_t)$ be a diffusion process on $\mathbb{R}\times\mathcal{A}$. Assume that $\eta_t$ has station…

Self-reinforced diffusion conjecture. If $\sum_{k=1}^{n}k^2a_k<0$, then $X_t$ converges almost surely; if $\sum_{k=1}^{n}k^2a_k>0$, then