Dimers and cluster integrable systems

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph. The sum of Hamiltonians is essentially the partition function of the dimer model. Any graph on a torus gives rise to a bipartite graph on the torus. We show that the phase space of the latter has a Lagrangian subvariety. We identify it with the space parametrizing resistor networks on the original graph.We construct several discrete quantum integrable systems.Comment: This is an updated version, 75 pages, which will appear in Ann. Sci. EN

Many New Hampshire Jobs Do Not Pay a Livable Wage

Two forces are likely to have the greatest impact on the projected availability of livable wage jobs in coming years. The first is the course of the current economic downturn. Table 11 shows the New England Economic Partnership (NEE P) forecast for New Hampshire's unemployment rate from 2008 to 2012. As the table shows, unemployment is projected to increase from 3.7 percent in 2007 to 4.2 percent in 2009, after which it is projected to gradually fall. The latest NEE P forecast predicted a relatively mild economic contraction, which provides some reason for optimism among New Hampshire workers. However, any optimism should be tempered by the fact that the latest forecast was issued before the dramatic stock market decline and at the beginning of the financial crisis.The second major factor impacting the availability of livable wage jobs is the changing composition of New Hampshire's economic base. Between 2000 and 2007, New Hampshire lost 25,400 manufacturing jobs, representing a 25 percent decline in the industry.10 Over the same period, jobs in education, healthcare, retail trade, and leisure and hospitality grew by about the same number of jobs. To the extent New Hampshire continues in this transition from a production-based to a service-based economy, the proportion of livable wage jobs is expected to decline

Pattern densities in fluid dimer models

In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for liquid and gaseous Gibbs measures of the dimer model, and prove that they converge to a linear combination of a derivative of the Gaussian massless free field and an independent white noise.Comment: 38 pages, 3 figure

Random skew plane partitions with a piecewise periodic back wall

Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in [OR2], but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in [OR2] is singular. We also observe the bead process introduced in [B] appearing in the asymptotics at the top of the limit shape.Comment: 24 pages. This version to appear in Annales Henri Poincar

A Study of Proton Induced Effects on Reflective Surfaces of Space Mirrors

Proton radiation effects at synchronous earth orbits on telescope mirror reflective surfaces and substrate

STORAGE UTILIZATION IN A DEFICIT REGION

Crop Production/Industries,

Scaling limits of random skew plane partitions with arbitrarily sloped back walls

The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk are given by the incomplete Beta kernel, as expected. As a consequence it is established that the local correlation functions in the scaling limit do not depend on the particular sequence of discrete inner shapes that converge to V. A detailed analysis of the correlation kernels at the top of the limit shape and of the frozen boundary is given. It is shown that depending on the slope of the linear section of the back wall, the system exhibits behavior observed in either [OR2] or [BMRT].Comment: 29 pages. Version 2: Several sections and proofs were improved and completely rewritten. These include Sections 2.2.2,2.2.4 and 2.2.5, Lemmas 2.3 and 4.2, and Proposition 4.1. Section 1.1.3 was added. This version is to be published in Comm. Math. Phy