English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We elucidate the close connection between the repulsive lattice gas inequilibrium statistical mechanics and the Lovasz local lemma in probabilisticcombinatorics. We show that the conclusion of the Lovasz local lemma holds fordependency graph G and probabilities {p_x} if and only if the independent-setpolynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore,we show that the usual proof of the Lovasz local lemma -- which provides asufficient condition for this to occur -- corresponds to a simple inductiveargument for the nonvanishing of the independent-set polynomial in a polydisc,which was discovered implicitly by Shearer and explicitly by Dobrushin. We alsopresent some refinements and extensions of both arguments, including ageneralization of the Lovasz local lemma that allows for "soft" dependencies.In addition, we prove some general properties of the partition function of arepulsive lattice gas, most of which are consequences of the alternating-signproperty for the Mayer coefficients. We conclude with a brief discussion of therepulsive lattice gas on countably infinite graphs.Comment: LaTex2e, 97 pages. Version 2 makes slight changes to improve clarity.  To be published in J. Stat. Phy

The Repulsive Lattice Gas, the Independent-Set Polynomial, and the Lov�sz Local Lemma