2 problems

Let $E(t)={\mathbf E}(X(t)^2)$, and suppose that for some $-1<\alpha<1$ the infrared bounds … hold. Diffusivity exponent conjecture. Under these conditions, the true asymptotic ord…

Durrett–Rogers law of large numbers conjecture. Under these assumptions, $X(t)/t\to0$ almost surely. This conjecture concerns the long-time displacement of a one-dimensional self-i…