8 papers
Equality conditions for correlation inequalities
Swee Hong Chan, Igor Pak
We prove equality conditions for the Ahlswede--Daykin (AD) inequality and the Fortuin--Kasteleyn--Ginibre (FKG) inequality. We then present a number of applications and special cas…
Correlation inequalities for Schur positivity
Swee Hong Chan, Hong Chen, Igor Pak +1
We generalize the Ahlswede--Daykin inequality (1978) to a Schur positive \emph{ADS inequality}, which also contains the Lam--Postnikov--Pylyavskyy inequality (2007) as a special ca…
Independent Sets and Continued Fractions
Swee Hong Chan, Steven Heilman, Greta Panova
Linek's 1989 problem asks whether the numbers of independent sets of trees avoid infinitely many positive integers. We show that the set of natural numbers realized as the number o…
Normalized matching property for competing urn models
Swee Hong Chan
We study the competing urn model in which balls are placed independently into urns according to (possibly distinct) ball distributions. Kahn and Neiman (2010) showed that,…
Unimodality for Radon partitions of random vectors
Swee Hong Chan, Gil Kalai, Bhargav Narayanan +2
Consider the (almost surely) unique Radon partition of a set of random Gaussian vectors in ; choose one of the two parts of this partition uniformly at random,…
Spanning trees and continued fractions
Swee Hong Chan, Alex Kontorovich, Igor Pak
We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on vertices, answering a question of SedláÄek from 19…