25 research outputs found
LERW as an example of off-critical SLEs
Two dimensional loop erased random walk (LERW) is a random curve, whose
continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter
kappa=2. In this article we study ``off-critical loop erased random walks'',
loop erasures of random walks penalized by their number of steps. On one hand
we are able to identify counterparts for some LERW observables in terms of
symplectic fermions (c=-2), thus making further steps towards a field theoretic
description of LERWs. On the other hand, we show that it is possible to
understand the Loewner driving function of the continuum limit of off-critical
LERWs, thus providing an example of application of SLE-like techniques to
models near their critical point. Such a description is bound to be quite
complicated because outside the critical point one has a finite correlation
length and therefore no conformal invariance. However, the example here shows
the question need not be intractable. We will present the results with emphasis
on general features that can be expected to be true in other off-critical
models.Comment: 45 pages, 2 figure
Multiple drivers of decline in the global status of freshwater crayfish (Decapoda: Astacidea)
International audienceRates of biodiversity loss are higher in freshwater ecosystems than in most terrestrial or marine ecosystems, making freshwater conservation a priority. However, prioritization methods are impeded by insufficient knowledge on the distribution and conservation status of freshwater taxa, particularly invertebrates. We evaluated the extinction risk of the world's 590 freshwater crayfish species using the IUCN Categories and Criteria and found 32% of all species are threatened with extinction. The level of extinction risk differed between families, with proportionally more threatened species in the Parastacidae and Astacidae than in the Cambaridae. Four described species were Extinct and 21% were assessed as Data Deficient. There was geographical variation in the dominant threats affecting the main centres of crayfish diversity. The majority of threatened US and Mexican species face threats associated with urban development, pollution, damming and water management. Conversely, the majority of Australian threatened species are affected by climate change, harvesting, agriculture and invasive species. Only a small proportion of crayfish are found within the boundaries of protected areas, suggesting that alternative means of long-term protection will be required. Our study highlights many of the significant challenges yet to come for freshwater biodiversity unless conservation planning shifts from a reactive to proactive approach