From Particle Systems to Partial Differential Equations III : Particle Systems and PDEs III Braga Portugal December 2014 The main focus of this book is on different topics in probability theory partial differential equations and kinetic theory presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics engineering chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations held at the University of Minho Braga Portugal in December 2014. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations providing a venue for them to present their latest findings and discuss their areas of expertise. Further it was intended to introduce a vast and varied public including young researchers to the subject of interacting particle systems its underlying motivation and its relation to partial differential equations. This book will appeal to probabilists analysts and those mathematicians whose work involves topics in mathematical physics stochastic processes and differential equations in general as well as those physicists whose work centers on statistical mechanics and kinetic theory. Convergence of Diffusion Drift Many Particle Systems in Probability under a Sobolev Norm Global asymptotic stability of a general nonautonomous Cohen Grossberg model with unbounded ampliﬁcation functions Modelling of systems with a dispersed phase: “measuring” small sets in the presence of elliptic operators From market data to agent based models and stochastic differential equations Entropy dissipation estimates for the Landau equation: General cross sections Phase transitions and coarse graining for a system of particles in the continuum Sub–shock formation in reacting gas mixtures The gradient ﬂow approach to hydrodynamic limits for the simple exclusion process The gradient ﬂow approach to hydrodynamic limits for the simple exclusion process Hydrodynamic limit of quantum random walks Derivation of the Boltzmann equation: hard spheres short range potentials and beyond Duality relations for the periodic ASEP conditioned on a low current Asymptotics for FBSDES with Jumps and Connections with Partial Integral Differential Equations The Boltzmann Equation over RD: Dispersion vs Dissipation.