19,613 research outputs found
Subdiffusivity of a random walk among a Poisson system of moving traps on
We consider a random walk among a Poisson system of moving traps on . In earlier work [DGRS12], the quenched and annealed survival probabilities
of this random walk have been investigated. Here we study the path of the
random walk conditioned on survival up to time in the annealed case and
show that it is subdiffusive. As a by-product, we obtain an upper bound on the
number of so-called thin points of a one-dimensional random walk, as well as a
bound on the total volume of the holes in the random walk's range
Affine Macdonald conjectures and special values of Felder-Varchenko functions
We refine the statement of the denominator and evaluation conjectures for
affine Macdonald polynomials proposed by Etingof-Kirillov Jr. and prove the
first non-trivial cases of these conjectures. Our results provide a
q-deformation of the computation of genus 1 conformal blocks via elliptic
Selberg integrals by Felder-Stevens-Varchenko. They allow us to give precise
formulations for the affine Macdonald conjectures in the general case which are
consistent with computer computations.
Our method applies recent work of the second named author to relate these
conjectures in the case of to evaluations of
certain theta hypergeometric integrals defined by Felder-Varchenko. We then
evaluate the resulting integrals, which may be of independent interest, by
well-chosen applications of the elliptic beta integral introduced by
Spiridonov.Comment: 26 pages. v3: minor edits for published versio
A failure of meiotic chromosome segregation in a fbh1Ī mutant correlates with persistent Rad51-DNA associations
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