Birthday Inequalities, Repulsion, and Hard Spheres
@article{Perkins2015BirthdayIR,
title={Birthday Inequalities, Repulsion, and Hard Spheres},
author={Will Perkins},
journal={arXiv: Probability},
year={2015}
}We study a birthday inequality in random geometric graphs: the probability of the empty graph is upper bounded by the product of the probabilities that each edge is absent. We show the birthday inequality holds at low densities, but does not hold in general. We give three different applications of the birthday inequality in statistical physics and combinatorics: we prove lower bounds on the free energy of the hard sphere model and upper bounds on the number of independent sets and matchings of… CONTINUE READING
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- 1
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- Mathematics, Computer Science
- Electron. Notes Discret. Math.
- 2017
- 6
- PDF
Independent sets, matchings, and occupancy fractions
- Mathematics, Computer Science
- J. Lond. Math. Soc.
- 2017
- 36
- PDF
Polymer dynamics via cliques with applications to hard-sphere mixtures
- Mathematics, Computer Science
- ArXiv
- 2020
Phase Transitions for Detecting Latent Geometry in Random Graphs
- Mathematics, Computer Science
- ArXiv
- 2019
- 3
- PDF
Perfect simulation of the Hard Disks Model by Partial Rejection Sampling
- Mathematics, Computer Science
- ICALP
- 2018
- 12
- PDF
References
SHOWING 1-10 OF 28 REFERENCES
Lower Bounds on the Critical Density in the Hard Disk Model via Optimized Metrics
- Computer Science, Mathematics
- ArXiv
- 2014
- 6
- PDF
Matchings and independent sets of a fixed size in regular graphs
- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2009
- 32
- PDF
An Entropy Approach to the Hard-Core Model on Bipartite Graphs
- Mathematics, Computer Science
- Comb. Probab. Comput.
- 2001
- 145
- Highly Influential
Asymptotics of the Upper Matching Conjecture
- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2013
- 11
- Highly Influential
- PDF