Burdzy, KrzysztofChen, Shuntao2024-04-262024-04-262024Chen_washington_0250E_26562.pdfhttp://hdl.handle.net/1773/51375Thesis (Ph.D.)--University of Washington, 2024In the foldings part, we estimated the convergence rate for the folding model on the unit sphere in R^n. This is a toy model for the coupling approach to the convergence rate in densely packed pinned billiard balls on a torus. In the particle collisions part, we gave the asymptotic formula for the collision location of two sample particles with fixed initial locations and velocities distributed according to the microcanonical ensemble formula.application/pdfen-USCC BY-NC-SAMathematicsMathematicsThesis