14 citations · 54 across the 14 of their papers we have counts for
11 papers · 1 filter
Infinite-mean Galton-Watson trees have zero random-interchange threshold
Andreas Klippel, Benjamin Lees, Christian Mönch
We prove that, on a Galton-Watson tree with almost surely finite offspring and infinite offspring mean, the random interchange process has critical parameter zero for infinite cycl…
Rainbow percolation
Peter Gracar, Benjamin Lees
We consider the weight-dependent random connection model on a Poisson point process of intensity on in which the vertices and are joined…
Loop vs. Bernoulli percolation on trees: strict inequality of critical values
Andreas Klippel, Benjamin Lees, Christian Mönch
We study loop ensembles on locally finite rooted trees. The loops are induced by a Poisson process of links on the edges; the transposition-only case is the random interchange proc…
Combinatorial identities from an inhomogeneous Ising chain
Jessica Jay, Benjamin Lees
We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove…
Griffiths inequalities for the -spin model
Benjamin Lees
We prove Griffiths inequalities for the -spin model with inhomogeneous coupling constants and external magnetic field for any . This is achieved by using a represent…
Correlation inequalities for the uniform 8-vertex model and the toric code model
Jakob E. Björnberg, Benjamin Lees
We elucidate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk…
Exponential decay of transverse correlations for O(N) spin systems and related models
Benjamin Lees, Lorenzo Taggi
We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N > 1. Our…
Site-monotonicity properties for reflection positive measures with applications to quantum spin systems
Benjamin Lees, Lorenzo Taggi
We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity p…
Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N
Benjamin Lees, Lorenzo Taggi
We provide a uniformly-positive point-wise lower bound for the two-point function of the classical spin model on the torus of , , when $N \in \mathbb…
Sharp phase transition for random loop models on trees
Volker Betz, Johannes Ehlert, Benjamin Lees +1
We investigate the random loop model on the -ary tree. For , we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive r…
The interchange process with reversals on the complete graph
Jakob E. Björnberg, Michał Kotowski, Benjamin Lees +1
We consider an extension of the interchange process on the complete graph, in which a fraction of the transpositions are replaced by `reversals'. The model is motivated by statisti…