Estimates of random walk exit probabilities and application to loop-erased random walk

We prove an estimate for the probability that a simple random walk in a simply connected subset A of Z^2 starting on the boundary exits A at another specified boundary point. The estimates are uniform over all domains of a given inradius. We apply these estimates to prove a conjecture of S. Fomin in 2001 concerning a relationship between crossing probabilities of loop-erased random walk and Brownian motion.Comment: 26 pages, 0 figure

The Green's function for the radial Schramm-Loewner evolution

We prove the existence of the Green's function for radial SLE(k) for k<8. Unlike the chordal case where an explicit formula for the Green's function is known for all values of k<8, we give an explicit formula only for k=4. For other values of k, we give a formula in terms of an expectation with respect to SLE conditioned to go through a point.Comment: v1: 16 pages, 0 figure

The Preventative Healthcare Shortage: A Look at the VT and CT Community Perspectives and Medical Student Interest

We adapted and modified a previously generated survey to better understand the motivations and barriers of medical students to enter primary care. The survey was dispersed to all medical students at LCOM as well as third and fourth year medical students at Ross University and American University of the Caribbean (AUC). We analyzed preliminary data from 100 respondents. Notable barriers identified included cost of medical school, stigma associated with primary care, and inadequate time spent with patients. Recommendations for possible intervention were discussed.https://scholarworks.uvm.edu/fmclerk/1930/thumbnail.jp

Atmospheric fungal nanoparticle bursts.

Aerosol nanoparticles play an important role in the climate system by affecting cloud formation and properties, as well as in human health because of their deep reach into lungs and the circulatory system. Determining nanoparticle sources and composition is a major challenge in assessing their impacts in these areas. The sudden appearance of large numbers of atmospheric nanoparticles is commonly attributed to secondary formation from gas-phase precursors, but in many cases, the evidence for this is equivocal. We report the detection of a mode of fungal fragments with a mobility diameter of roughly 30 nm released in episodic bursts in ambient air over an agricultural area in northern Oklahoma. These events reached concentrations orders of magnitude higher than other reports of biological particles and show similarities to unclarified events reported previously in the Amazon. These particles potentially represent a large source of both cloud-forming ice nuclei and respirable allergens in a variety of ecosystems