Correlation bounds for fields and matroids

  • June Huh

    Princeton University, USA
  • Benjamin Schröter

    KTH Royal Institute of Technology, Stockholm, Sweden
  • Botong Wang

    University of Wisconsin-Madison, USA
Correlation bounds for fields and matroids cover
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Let G be a finite connected graph, and let T be a spanning tree of G chosen uniformly at random. The work of Kirchhoff on electrical networks can be used to show that the events and are negatively correlated for any distinct edges and . What can be said for such events when the underlying matroid is not necessarily graphic? We use Hodge theory for matroids to bound the correlation between the events , where B is a randomly chosen basis of a matroid. As an application, we prove Mason’s conjecture that the number of -element independent sets of a matroid forms an ultra-log-concave sequence in .

Cite this article

June Huh, Benjamin Schröter, Botong Wang, Correlation bounds for fields and matroids. J. Eur. Math. Soc. 24 (2022), no. 4, pp. 1335–1351

DOI 10.4171/JEMS/1119