Coexistence, enhancements and short loops in random walk loop soups

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Cites Work

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Phase transition in loop percolation
Random walk loop soups and conformal loop ensembles
Markovian loop clusters on graphs
The mathematics of the Bose gas and its condensation.
Spatial random permutations with small cycle weights
The Brownian loop soup
Shifted critical threshold in the loop \(O(n)\) model at arbitrarily small \(n\)
Exponential decay in the loop \(O(n)\) model on the hexagonal lattice for \(n > 1\) and \(x<\frac{1}{\sqrt{3}}+\varepsilon (n)\)
Exponential decay of transverse correlations for \(O(N)\) spin systems and related models
Interacting self-avoiding polygons
Site monotonicity and uniform positivity for interacting random walks and the spin \(O(N)\) model with arbitrary \(N\)
Asymptotic statistics of cycles in surrogate-spatial permutations
Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup
Loop correlations in random wire models
Scaling limit of ballistic self-avoiding walk interacting with spatial random permutations
Limit distributions for Euclidean random permutations
Spatial random permutations and infinite cycles
The sampling theory of selectively neutral alleles
An elementary proof of phase transition in the planar XY model
Lectures on the Spin and Loop O(n) Models
Uniformly Positive Correlations in the Dimer Model and Macroscopic Interacting Self‐Avoiding Walk in ℤ^d, d ≥ 3
On the Spatial Markov Property of Soups of Unoriented and Oriented Loops
Statistical Mechanics of Lattice Systems
Atomic Theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi></mml:math>Transition in Helium
Macroscopic loops in the Bose gas, spin \(O(N)\) and related models
Formation of infinite loops for an interacting bosonic loop soup
About systems of vectors and subspaces in finite dimensional space recovering vectorsignal