Lower bounds for integral functionals generated by bipartite graphs

Barbara Kaskosz; Lubos Thoma

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 2, page 571-592
  • ISSN: 0011-4642

Abstract

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We study lower estimates for integral fuctionals for which the structure of the integrand is defined by a graph, in particular, by a bipartite graph. Functionals of such kind appear in statistical mechanics and quantum chemistry in the context of Mayer's transformation and Mayer's cluster integrals. Integral functionals generated by graphs play an important role in the theory of graph limits. Specific kind of functionals generated by bipartite graphs are at the center of the famous and much studied Sidorenko's conjecture, where a certain lower bound is conjectured to hold for every bipartite graph. In the present paper we work with functionals more general and lower bounds significantly sharper than those in Sidorenko's conjecture. In his 1991 seminal paper, Sidorenko proved such sharper bounds for several classes of bipartite graphs. To obtain his result he used a certain way of ``gluing'' graphs. We prove his inequality for a new class of bipartite graphs by defining a different type of gluing.

How to cite

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Kaskosz, Barbara, and Thoma, Lubos. "Lower bounds for integral functionals generated by bipartite graphs." Czechoslovak Mathematical Journal 69.2 (2019): 571-592. <http://eudml.org/doc/294493>.

@article{Kaskosz2019,
abstract = {We study lower estimates for integral fuctionals for which the structure of the integrand is defined by a graph, in particular, by a bipartite graph. Functionals of such kind appear in statistical mechanics and quantum chemistry in the context of Mayer's transformation and Mayer's cluster integrals. Integral functionals generated by graphs play an important role in the theory of graph limits. Specific kind of functionals generated by bipartite graphs are at the center of the famous and much studied Sidorenko's conjecture, where a certain lower bound is conjectured to hold for every bipartite graph. In the present paper we work with functionals more general and lower bounds significantly sharper than those in Sidorenko's conjecture. In his 1991 seminal paper, Sidorenko proved such sharper bounds for several classes of bipartite graphs. To obtain his result he used a certain way of ``gluing'' graphs. We prove his inequality for a new class of bipartite graphs by defining a different type of gluing.},
author = {Kaskosz, Barbara, Thoma, Lubos},
journal = {Czechoslovak Mathematical Journal},
keywords = {integral inequality; bipartite graph; graph homomorphism; Sidorenko's conjecture},
language = {eng},
number = {2},
pages = {571-592},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lower bounds for integral functionals generated by bipartite graphs},
url = {http://eudml.org/doc/294493},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Kaskosz, Barbara
AU - Thoma, Lubos
TI - Lower bounds for integral functionals generated by bipartite graphs
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 571
EP - 592
AB - We study lower estimates for integral fuctionals for which the structure of the integrand is defined by a graph, in particular, by a bipartite graph. Functionals of such kind appear in statistical mechanics and quantum chemistry in the context of Mayer's transformation and Mayer's cluster integrals. Integral functionals generated by graphs play an important role in the theory of graph limits. Specific kind of functionals generated by bipartite graphs are at the center of the famous and much studied Sidorenko's conjecture, where a certain lower bound is conjectured to hold for every bipartite graph. In the present paper we work with functionals more general and lower bounds significantly sharper than those in Sidorenko's conjecture. In his 1991 seminal paper, Sidorenko proved such sharper bounds for several classes of bipartite graphs. To obtain his result he used a certain way of ``gluing'' graphs. We prove his inequality for a new class of bipartite graphs by defining a different type of gluing.
LA - eng
KW - integral inequality; bipartite graph; graph homomorphism; Sidorenko's conjecture
UR - http://eudml.org/doc/294493
ER -

References

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