C. Monthus

Real-Space renormalization for the drawups and drawdowns of stochastic trajectories: universality classes for diffusion processes and random walks via the scale function

For one-dimensional diffusion processes with arbitrary diffusion coefficient $D(x)$ and Ito force $F_I(x)$, we analyze the statistical properties of the renormalized trajectories at scale $\Gamma$, where one keeps only the alternating sequence of local minima and local maxima that are separated by drawups and drawdowns...