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Monotonicity of correlations for general loop soups

Oberseminar Darmstadt

Datum: 06.06.2019

Zeit: 16:15–17:45 Uhr


Loop soup models involve one dimensional objects (loops/walks/dimers) living in a higher dimensional space. These models are connected to various spin and particle systems from statistical mechanics.

A general loop soup model on the hypercubic lattice will be introduced and specific cases corresponding to models such as the $O(N)$-loops and  -spin model, the dimer and double dimer model, and spatial random permutations will be explained.

A general monotonicity result for correlations in this model will be presented and, in the special case of the $O(N)$-spin model it will be shown that this provides a proof of monotonicity for two point correlations as a function of the distance between particles, providing a positive answer to a well accepted, but long standing conjecture in the case $N\geq 3$.


Ben Lees, TU Darmstadt


TU Darmstadt S2|15 Raum 401
Schlossgartenstr. 7, 64289 Darmstadt


Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381


Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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