The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Experimental and Modeled Assessment of Interventions to Reduce PM2.5 in a Residence during aWildfire Event

Increasingly large and frequent wildfires affect air quality even indoors by emitting and dispersing fine/ultrafine particulate matter known to pose health risks to residents. With this health threat, we are working to help the building science community develop simplified tools that may be used to estimate impacts to large numbers of homes based on high-level housing characteristics. In addition to reviewing literature sources, we performed an experiment to evaluate interventions to mitigate degraded indoor air quality. We instrumented one residence for one week during an extreme wildfire event in the Pacific Northwest. Outdoor ambient concentrations of PM2.5 reached historic levels, sustained at over 200 μg/m3 for multiple days. Outdoor and indoor PM2.5 were monitored, and data regarding building characteristics, infiltration, and mechanical system operation were gathered to be consistent with the type of information commonly known for residential energy models. Two conditions were studied: a high-capture minimum efficiency rated value (MERV 13) filter integrated into a central forced air (CFA) system, and a CFA with MERV 13 filtration operating with a portable air cleaner (PAC). With intermittent CFA operation and no PAC, indoor corrected concentrations of PM2.5 reached 280 μg/m3, and indoor/outdoor (I/O) ratios reached a mean of 0.55. The measured I/O ratio was reduced to a mean of 0.22 when both intermittent CFA and the PAC were in operation. Data gathered from the test home were used in a modeling exercise to assess expected I/O ratios from both interventions. The mean modeled I/O ratio for the CFA with an MERV 13 filter was 0.48, and 0.28 when the PAC was added. The model overpredicted the MERV 13 performance and underpredicted the CFA with an MERV 13 filter plus a PAC, though both conditions were predicted within 0.15 standard deviation. The results illustrate the ways that models can be used to estimate indoor PM2.5 concentrations in residences during extreme wildfire smoke events

Lichens of six vernal pools in Acadia National Park, ME, USA

Whereas lichen-habitat relations have been well-documented globally, literature on lichens of vernal pools is scant. We surveyed six vernal pools at Acadia National Park on Mount Desert Island, Maine, USA for their lichen diversity. Sixty-seven species were identified, including seven species that are new reports for Acadia National Park: Fuscidea arboricola, Hypogymnia incurvoides, Lepraria finkii, Phaeographis inusta, Ropalospora viridis, Usnea flammea, and Violella fucata. Five species are considered uncommon or only locally common in New England: Everniastrum catawbiense, Hypogymnia krogiae, Pseudevernia cladonia, Usnea flammea, and Usnea merrillii. This work represents the first survey of lichens from vernal pools in Acadia National Park and strongly suggests that previous efforts at documenting species at the Park have underestimated its species diversity. More work should be conducted to determine whether a unique assemblage of lichens occurs in association with this unique habitat type

Influence of ion implantation on the magnetic and transport properties of manganite films

We have used oxygen ions irradiation to generate controlled structural disorder in thin manganite films. Conductive atomic force microscopy CAFM), transport and magnetic measurements were performed to analyze the influence of the implantation process in the physical properties of the films. CAFM images show regions with different conductivity values, probably due to the random distribution of point defect or inhomogeneous changes of the local Mn3+/4+ ratio to reduce lattice strains of the irradiated areas. The transport and magnetic properties of these systems are interpreted in this context. Metal-insulator transition can be described in the frame of a percolative model. Disorder increases the distance between conducting regions, lowering the observed TMI. Point defect disorder increases localization of the carriers due to increased disorder and locally enhanced strain field. Remarkably, even with the inhomogeneous nature of the samples, no sign of low field magnetoresistance was found. Point defect disorder decreases the system magnetization but doesn t seem to change the magnetic transition temperature. As a consequence, an important decoupling between the magnetic and the metal-insulator transition is found for ion irradiated films as opposed to the classical double exchange model scenario.Comment: 27 pages, 11 Figure

Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit

The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr package

AT 2017be - a new member of the class of Intermediate-Luminosity Red Transients

We report the results of our spectrophotometric monitoring campaign for AT~2017be in NGC~2537. Its lightcurve reveals a fast rise to an optical maximum, followed by a plateau lasting about 30 days, and finally a fast decline. Its absolute peak magnitude ($M_{r}$ $\simeq$ $-$12 $\rm{mag}$) is fainter than that of core-collapse supernovae, and is consistent with those of supernova impostors and other Intermediate-Luminosity Optical Transients. The quasi-bolometric lightcurve peaks at $\sim$ 2 $\times$ 10$^{40}$ erg s$^{-1}$, and the late-time photometry allows us to constrain an ejected $^{56}$Ni mass of $\sim$ 8 $\times$ 10$^{-4}$\msun. The spectra of AT~2017be show minor evolution over the observational period, a relatively blue continuum showing at early phases, which becomes redder with time. A prominent H$\alpha$ emission line always dominates over other Balmer lines. Weak Fe {\sc ii} features, Ca~{\sc ii} H$\&$K and the Ca {\sc ii} NIR triplet are also visible, while P-Cygni absorption troughs are found in a high resolution spectrum. In addition, the [Ca~{\sc ii}] $\lambda$7291,7324 doublet is visible in all spectra. This feature is typical of Intermediate-Luminosity Red Transients (ILRTs), similar to SN~2008S. The relatively shallow archival Spitzer data are not particularly constraining. On the other hand, a non-detection in deeper near-infrared HST images disfavours a massive Luminous Blue Variable eruption as the origin for AT~2017be. As has been suggested for other ILRTs, we propose that AT~2017be is a candidate for a weak electron-capture supernova explosion of a super-asymptotic giant branch star, still embedded in a thick dusty envelope.Comment: 21 pages, 15 figures, accepted by MNRA

Random Planar Lattices and Integrated SuperBrownian Excursion

In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE. More generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ISE shifted to set the minimum of its support in zero. The first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's well labelled trees. The second step relates these trees to embedded (discrete) trees in the sense of Aldous, via the conjugation of tree principle, an analogue for trees of Vervaat's construction of the Brownian excursion from the bridge. From probability theory, we need a new result of independent interest: the weak convergence of the encoding of a random embedded plane tree by two contour walks to the Brownian snake description of ISE. Our results suggest the existence of a Continuum Random Map describing in term of ISE the scaled limit of the dynamical triangulations considered in two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and http://www.iecn.u-nancy.fr/~chassain