On Brownian limits of planar trees and maps with a prescribed degree sequence

We study a configuration model on bipartite planar maps where, given $n$ even integers, one samples a planar map uniformly at random with these face degrees. We prove that when suitably rescaled, such maps always admit subsequential limits as $n \to \infty$ in the Gromov-Hausdorff-Prokhorov topology. Further, we show that they converge in distribution towards the celebrated Brownian map, and more generally a Brownian disk for maps with a boundary, if and only if there is no inner face with a macroscopic degree, or, if the perimeter is too big, the maps degenerate and converge to the Brownian CRT. The latter case include that of size-conditioned Boltzmann map associated with critical weights in the domain of attraction of a Cauchy distribution, which was missing in the literature. Our proofs rely on bijections with random labelled plane trees, which are similarly sampled uniformly given $n$ outdegrees. Along the way, we obtain some results on the geometry of such trees, such as a convergence to the Brownian CRT but only in the weaker sense of subtrees spanned by random vertices, which are of independent interest.Comment: The previous version has been merged with arXiv:1902.0453

Forest disturbance and recovery: A general review in the context of spaceborne remote sensing of impacts on aboveground biomass and canopy structure

Abrupt forest disturbances generating gaps \u3e0.001 km2 impact roughly 0.4–0.7 million km2a−1. Fire, windstorms, logging, and shifting cultivation are dominant disturbances; minor contributors are land conversion, flooding, landslides, and avalanches. All can have substantial impacts on canopy biomass and structure. Quantifying disturbance location, extent, severity, and the fate of disturbed biomass will improve carbon budget estimates and lead to better initialization, parameterization, and/or testing of forest carbon cycle models. Spaceborne remote sensing maps large-scale forest disturbance occurrence, location, and extent, particularly with moderate- and fine-scale resolution passive optical/near-infrared (NIR) instruments. High-resolution remote sensing (e.g., ∼1 m passive optical/NIR, or small footprint lidar) can map crown geometry and gaps, but has rarely been systematically applied to study small-scale disturbance and natural mortality gap dynamics over large regions. Reducing uncertainty in disturbance and recovery impacts on global forest carbon balance requires quantification of (1) predisturbance forest biomass; (2) disturbance impact on standing biomass and its fate; and (3) rate of biomass accumulation during recovery. Active remote sensing data (e.g., lidar, radar) are more directly indicative of canopy biomass and many structural properties than passive instrument data; a new generation of instruments designed to generate global coverage/sampling of canopy biomass and structure can improve our ability to quantify the carbon balance of Earth\u27s forests. Generating a high-quality quantitative assessment of disturbance impacts on canopy biomass and structure with spaceborne remote sensing requires comprehensive, well designed, and well coordinated field programs collecting high-quality ground-based data and linkages to dynamical models that can use this information

Rainfall but not selective logging affect changes in abundance of tropical forest butterfly in Sabah, Borneo

We investigated the effects of rainfall on the distribution and abundance of the satyrine butterfly Ragadia makuta in selectively logged and unlogged forest on Borneo. In 1997-98, there was a severe El Nino-Southern Oscillation (ENSO) drought, and annual surveys over a 4-y period showed that abundance of R. makuta was greatly reduced during the drought, but that populations quickly recovered after it. Monthly surveys over a 12-mo period of typical rainfall showed that high rainfall in the month preceding surveys significantly reduced butterfly abundance. Butterfly abundance and distribution did not differ between selectively logged and unlogged areas in either monthly or annual surveys and there was no difference between selectively logged and unlogged areas in the pattern of post-drought recovery. These results indicate that the abundance of R. makuta was significantly reduced both after high rainfall and during severe drought, but that these impacts were short-lived and were not affected by habitat disturbance. ENSO droughts on Borneo naturally often lead to widespread forest fires and thus impacts of ENSO events for butterflies are more likely to be due to indirect effects of habitat loss, rather than direct effects of drought on butterfly population dynamics

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure