The Parabolic Anderson Model with Acceleration and Deceleration

We describe the large-time moment asymptotics for the parabolic Anderson model where the speed of the diffusion is coupled with time, inducing an acceleration or deceleration. We find a lower critical scale, below which the mass flow gets stuck. On this scale, a new interesting variational problem arises in the description of the asymptotics. Furthermore, we find an upper critical scale above which the potential enters the asymptotics only via some average, but not via its extreme values. We make out altogether five phases, three of which can be described by results that are qualitatively similar to those from the constant-speed parabolic Anderson model in earlier work by various authors. Our proofs consist of adaptations and refinements of their methods, as well as a variational convergence method borrowed from finite elements theory.Comment: 19 page

Ginzburg-Landau vortices, Coulomb Gases, and Renormalized Energies

This is a review about a series of results on vortices in the Ginzburg-Landau model of superconductivity on the one hand, and point patterns in Coulomb gases on the other hand, as well as the connections between the two topics.Comment: review paper, submitted to J. Stat. Phy

Sexual Autonomy and Violence Against Women

Our position is that the threat and experience of violence that sex workers face is a crucial issue to address and should be considered in debates concerning the legalization of prostitution because even in countries where prostitution is legalized, prostitutes continue to experience violence. Our focus is to show that violence is crucially important to address because both the experience and the fear of physical, sexual or psychological harm erodes women ’s capacity to choose and act autonomously. We shall argue, then, that despite differences between inside and outside prostitution, all women in prostitution suffer unacceptable levels of violence ; hence, we conclude that all forms of prostitution continue to be morally problemati