Hydrodynamic scaling limit of continuum solid-on-solid model

Interacting particle systems are stochastic processes proposed by statistical mechanics for the movement of particles at the microscopic scale, with the aim to explain certain physical phenomena. The book discuses the continuum solid-on-solid model, also known as the fourth-order Ginzurg-Landau model, a model developed to understand the relaxation to equilibrium of a crystal surface through diffusion. With rigorous arguments the hydrodynamic scaling limit of continuum solid-on-solid model is shown to be a fourth-order, nonlinear partial differential equation. The fluctuation-dissipation equation of the model is established due to the mathematical result that the model exact functions form a subspace of codimension one in the space of closed functions. Connections between the spaces of closed and exact functions for the second-order Ginzburg-Landau model and algebraic topology are described.

Autorentext

Anamaria Savu received her PhD from the University of Toronto for her research in the area of interacting particle systems, a large and growing field of probability theory. She then pursued postdoctoral studies at Queen's University and University of Alberta. Currently she works on statistical methodologies for research in health sciences.