John Pardon
Central limit theorems for uniform model random polygons.
Thu, 10/27/2011 - 15:01 — SomNambulAuthors: John Pardon
Subjects: Probability
AbstractWe show how a central limit theorem for Poisson model random polygons implies
a central limit theorem for uniform model random polygons. To prove this
implication, it suffices to show that in the two models, the variables in
question have asymptotically the same expectation and variance. We use integral
geometric expressions for these expectations and variances to reduce the
desired estimates to the convergence $(1+\frac\alpha n)^n\to e^\alpha$ as
$n\to\infty$.The link concordance invariant from Lee homology.
Tue, 07/26/2011 - 15:01 — SomNambulAuthors: John Pardon
Subjects: Geometric Topology
AbstractWe use the knot homology of Khovanov and Lee to construct link concordance
invariants generalizing the Rasmussen $s$-invariant of knots. The relevant
invariant for a link is a filtration on a vector space of dimension $2^{|L|}$.
The basic properties of the $s$-invariant all extend to the case of links; in
particular, any orientable cobordism $\Sigma$ between links induces a map
between their corresponding vector spaces which is filtered of degree
$\chi(\Sigma)$.
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