Subterranean Commodification: Informal Housing and the Legalization of Basement Suites in Vancouver from 1928 to 2009

This article draws on Margaret Radin's theorization of 'contested commodities' to explore the process whereby informal housing becomes formalized while also being shaped by legal regulation. In seeking to move once-informal housing into the domain of official legality, cities can seldom rely on a simple legal framework of private-law principles of property and contract. Instead, they face complex trade-offs between providing basic needs and affordability and meeting public-law norms around living standards, traditional neighbourhood feel and the environment. This article highlights these issues through an examination of the uneven process of legal formalization of basement apartments in Vancouver, Canada. We chose a lengthy period-from 1928 to 2009-to explore how basement apartments became a vital source of housing often at odds with city planning that has long favoured a low-density residential built form. We suggest that Radin's theoretical account makes it possible to link legalization and official market construction with two questions: whether to permit commodification and how to permit commodification. Real-world commodification processes-including legal sanction-reflect hybridization, pragmatic decision making and regulatory compromise. The resolution of questions concerning how to legalize commodification are also intertwined with processes of market expansion

Extremal statistics of curved growing interfaces in 1+1 dimensions

We study the joint probability distribution function (pdf) of the maximum M of the height and its position X_M of a curved growing interface belonging to the universality class described by the Kardar-Parisi-Zhang equation in 1+1 dimensions. We obtain exact results for the closely related problem of p non-intersecting Brownian bridges where we compute the joint pdf P_p(M,\tau_M) where \tau_M is there the time at which the maximal height M is reached. Our analytical results, in the limit p \to \infty, become exact for the interface problem in the growth regime. We show that our results, for moderate values of p \sim 10 describe accurately our numerical data of a prototype of these systems, the polynuclear growth model in droplet geometry. We also discuss applications of our results to the ground state configuration of the directed polymer in a random potential with one fixed endpoint.Comment: 6 pages, 4 figures. Published version, to appear in Europhysics Letters. New results added for non-intersecting excursion

On the dynamical behavior of the ABC model

We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature

Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size $\ell$ in contact with particle reservoirs at the boundary. We prove that, as for non--degenerate rates, the inverse of the spectral gap and the logarithmic Sobolev constant grow as $\ell^2$. It is also shown how one can obtain, via a scaling limit from the logarithmic Sobolev inequality, the exponential decay of a macroscopic entropy associated to a degenerate parabolic differential equation (porous media equation). We analyze finally the tagged particle displacement for the stationary process in infinite volume. In dimension larger than two we prove that, in the diffusive scaling limit, it converges to a Brownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure

Airy processes and variational problems

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI Proceedings: Topics in percolative and disordered systems

Invariance of the white noise for KdV

We prove the invariance of the mean 0 white noise for the periodic KdV. First, we show that the Besov-type space \hat{b}^s_{p, \infty}, sp <-1, contains the support of the white noise. Then, we prove local well-posedness in \hat{b}^s_{p, \infty} for p= 2+, s = -{1/2}+ such that sp <-1. In establishing the local well-posedness, we use a variant of the Bourgain spaces with a weight. This provides an analytical proof of the invariance of the white noise under the flow of KdV obtained in Quastel-Valko.Comment: 18 pages. To appear in Comm. Math. Phy

Endpoint distribution of directed polymers in 1+1 dimensions

We give an explicit formula for the joint density of the max and argmax of the Airy$_2$ process minus a parabola. The argmax has a universal distribution which governs the rescaled endpoint for large time or temperature of directed polymers in 1+1 dimensions.Comment: Expanded introductio

A pedestrian's view on interacting particle systems, KPZ universality, and random matrices

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo

A comprehensive review of oral glucosamine use and effects on glucose metabolism in normal and diabetic individuals

Glucosamine (GlcN) is a widely utilized dietary supplement that is used to promote joint health. Reports that oral GlcN supplementation at usual doses adversely affects glucose metabolism in subjects with impaired glucose tolerance have raised concerns that GlcN should be contraindicated in individuals with diabetes and those at risk for developing it. This review addresses its potential, when used at typical doses, to affect glucose metabolism and insulin sensitivity in healthy individuals and those with diabetes or ‘pre-diabetes’. Publicly available scientific information and data on GlcN were systematically compiled using the electronic search tool, Dialog®, and reviewed with special emphasis on human studies. In long-term clinical trials, including those containing subjects with type 2 diabetes or ‘pre-diabetes’, GlcN produced a non-significant lowering of fasting blood glucose concentrations in all groups of subjects treated for periods of up to 3 years. Owing to limitations in study design, conclusions based on studies that report adverse affects of GlcN on insulin sensitivity and glucose tolerance in pre-diabetic subjects are suspect. However, no definitive long-term studies of GlcN use for individuals with pre-diabetes are available. Nevertheless, based on available evidence, we conclude that GlcN has no effect on fasting blood glucose levels, glucose metabolism, or insulin sensitivity at any oral dose level in healthy subjects, individuals with diabetes, or those with impaired glucose tolerance

Large Deviations for the Stochastic Shell Model of Turbulence

In this work we first prove the existence and uniqueness of a strong solution to stochastic GOY model of turbulence with a small multiplicative noise. Then using the weak convergence approach, Laplace principle for so- lutions of the stochastic GOY model is established in certain Polish space. Thus a Wentzell-Freidlin type large deviation principle is established utilizing certain results by Varadhan and Bryc.Comment: 21 pages, submitted for publicatio