Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata

We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of Toom. They are defined as stochastic perturbations of cellular automata belonging to the category of monotonic binary tessellations and possessing a property of erosion. We prove, for a set of initial conditions, exponential convergence of the induced processes toward an extremal invariant measure with a highly predominant spin value. We also show that this invariant measure presents exponential decay of correlations in space and in time and is therefore strongly mixing.Comment: 21 pages, 0 figure, revised version including a generalization to a larger class of models, structure of the arguments unchanged, minor changes suggested by reviewers, added reference

Will Swing Pricing Save Sedentary Shareholders?

This Article explains and explores new Securities Exchange Commission rules authorizing optional swing pricing for mutual funds. Swing pricing is an anti-dilution tool intended to protect sedentary investors who enter, and stay, in a fund. Workers setting aside money for retirement are often sedentary investors. Mutual funds are the mainstay vehicle for retirement investors, yet as sedentary shareholders they can experience significant asset dilution over their savings lifetime. Swing pricing—a mutual fund pricing mechanism that allocates transaction costs to the triggering shareholders—could save sedentary shareholders, collectively, billions of dollars. The mutual fund industry’s operational complexities and competing regulatory obligations may prevent funds from immediately utilizing swing pricing once it becomes effective in November 2018. The biggest obstacle is a time conflict reminiscent of the chicken and egg problem. Under current industry operations, mutual funds will not receive the trading information necessary to adjust the daily price of the fund (swing the price) until after funds have to finalize the price adjustment. Blockchain technology—offering secure, automated, and verified ledgers—may present an operational path forward for the industry. The SEC’s swing pricing approach leaves unanswered how funds will overcome these, and other, hurdles. This Article explores the components of swing pricing, as well as the objections to and perceived benefits of swing pricing, and concludes with two unique perspectives on the SEC rules: one academic and one professional. This Article maintains that mutual funds should take on the challenge of implementing swing pricing, and that market incentives will pave the way

Harness processes and harmonic crystals

In the Hammersley harness processes the real-valued height at each site i in Z^d is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process "a la Harris" simultaneously for all times and boxes contained in Z^d. With this representation we compute covariances and show L^2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L^2 at speed t^{1-d/2} (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process.Comment: 21 pages. Revised version with minor changes. Version almost identical to the one to be published in SP

Stochastic theory of non-equilibrium wetting

We study a Langevin equation describing non-equilibrium depinning and wetting transitions. Attention is focused on short-ranged attractive substrate-interface potentials. We confirm the existence of first order depinning transitions, in the temperature-chemical potential diagram, and a tricritical point beyond which the transition becomes a non-equilibrium complete wetting transition. The coexistence of pinned and depinned interfaces occurs over a finite area, in line with other non-equilibrium systems that exhibit first order transitions. In addition, we find two types of phase coexistence, one of which is characterized by spatio-temporal intermittency (STI). A finite size analysis of the depinning time is used to characterize the different coexisting regimes. Finally, a stationary distribution of characteristic triangles or facets was shown to be responsible for the structure of the STI phase.Comment: To appear in Europhys. Lett. // 3 figure

Influence of transport and ocean ice extent on biogenic aerosol sulfur in the Arctic atmosphere

The recent decline in sea ice cover in the Arctic Ocean could affect the regional radiative forcing via changes in sea ice-atmosphere exchange of dimethyl sulfide (DMS) and biogenic aerosols formed from its atmospheric oxidation, such as methanesulfonic acid (MSA). This study examines relationships between changes in total sea ice extent north of 70 degrees N and atmospheric MSA measurement at Alert, Nunavut, during 1980-2009; at Barrow, Alaska, during 1997-2008; and at Ny-Alesund, Svalbard, for 1991-2004. During the 1980-1989 and 1990-1997 periods, summer (July-August) and June MSA concentrations at Alert decreased. In general, MSA concentrations increased at all locations since 2000 with respect to 1990 values, specifically during June and summer at Alert and in summer at Barrow and Ny-Alesund. Our results show variability in MSA at all sites is related to changes in the source strengths of DMS, possibly linked to changes in sea ice extent as well as to changes in atmospheric transport patterns. Since 2000, a late spring increase in atmospheric MSA at the three sites coincides with the northward migration of the marginal ice edge zone where high DMS emissions from ocean to atmosphere have previously been reported. Significant negative correlations are found between sea ice extent and MSA concentrations at the three sites during the spring and June. These results suggest that a decrease in seasonal ice cover influencing other mechanisms of DMS production could lead to higher atmospheric MSA concentrations

The effect of organic compounds on the growth rate of cloud droplets in marine and forest settings

International audienceOrganic matter represents an important fraction of the fine particle aerosol, yet our knowledge of the roles of organics in the activation of aerosol particles into cloud droplets is poor. A cloud condensation nucleus (CCN) counter is used to examine the relative growth rates of cloud droplets for case studies from field measurements on the North Pacific Ocean and in a coniferous forest. A model of the condensational growth of water droplets, on particles dissolving according to their solubility in water, is used to simulate the initial scattering of the droplets as they grow in the CCN counter. Simulations of the growth rates of fine particles sampled in the marine boundary layer of the North Pacific Ocean indicate that the main influence of the marine organic material on the water uptake rate is from its effect on the size distribution of the sulphate. Simulations of the observations of water uptake on biogenic organic aerosol particles sampled in a coniferous forest indicate an impact of the organic on the water uptake rates, but one that is still smaller than that of pure sulphate. The solubility of the organic becomes an important factor in determining the water uptake as the organic mass increases relative to sulphate. The values of the organic component of the hygroscopicity parameter ? that describes the CCN activity were found to be negligible for the marine particles and 0.02?0.05 for the forest particles

Generic two-phase coexistence in nonequilibrium systems

Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperature-magnetic-field phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite (n-dimensional) region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model [Toom,Geoff,GG], that exhibits generic bistability, i.e. two-phase coexistence over a finite region of its two-dimensional parameter space (see Section 1). In addition to its interest as a genuine nonequilibrium property, generic multistability, defined as a generalization of bistability, is both of practical and theoretical relevance. In particular, it has been used recently to argue that some complex structures appearing in nature could be truly stable rather than metastable (with important applications in theoretical biology), and as the theoretical basis for an error-correction method in computer science (see [GG,Gacs] for an illuminating and pedagogical discussion of these ideas).Comment: 7 pages, 6 figures, to appear in Eur. Phys. J. B, svjour.cls and svepj.clo neede

Multicomponent dynamical systems: SRB measures and phase transitions

We discuss a notion of phase transitions in multicomponent systems and clarify relations between deterministic chaotic and stochastic models of this type of systems. Connections between various definitions of SRB measures are considered as well.Comment: 13 pages, LaTeX 2

First order phase transition in a 1+1-dimensional nonequilibrium wetting process

A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics which generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the non-wet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters which define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the transition line.Comment: 4 pages, RevTeX, including 4 eps figure