1,720,961 research outputs found
Absorbing-state phase transition in biased activated random walk
Full text linkWe consider the activated random walk model on Zd, which undergoes a transition from an absorbing regime to a regime of sustained activity. A central question for this model involves the estimation of the critical density μc. We prove that if the jump distribution is biased, then μc < 1 for any sleeping rate λ, d ≥ 1, and that μc → 0 as λ → 0 in one dimension. This answers a question from Rolla and Sidoravicius (2012) and Dickman, Rolla and Sidoravicius (2010) in the case of biased jump distribution. Furthermore, we prove that the critical density depends on the jump distribution
Shifted critical threshold in the loop o(N) model at arbitrarily small n
Full text linkIn the loop O(n) model a collection of mutually-disjoint self-avoiding loops is drawn at random on a finite domain of a lattice with probability proportional to.where λ, n ∈ [0, ∞). Let μ be the connective constant of the lattice and, for any n ∈ [0, ∞), let λ c (n) be the largest value of λsuch that the loop length admits uniformly bounded exponential moments. It is not difficult to prove that λ c (n) = 1/μ when n = 0 (in this case the model corresponds to the self-avoiding walk) and that for any n ≥ 0, λ c (n) ≥ 1/μ. In this note we prove that,on Z d , with d ≥ 2, and on the hexagonal lattice, where c 0 > 0. This means that, when n is positive (even arbitrarily small), as a consequence of the mutual repulsion between the loops, a phase transition can only occur at a strictly larger critical threshold than in the self-avoiding walk
Critical density of activated random walks on transitive graphs
Full text linkWe consider the activated random walk model on general vertextransitive graphs. A central question in this model is whether the critical density μ c for sustained activity is strictly between 0 and 1. It was known that μ c > 0 on Z d, d = 1, and that μ c < 1 on Z for small enough sleeping rate. We show that μ c → 0 as λ → 0 in all vertex-transitive transient graphs, implying that μ c < 1 for small enough sleeping rate. We also show that μ c < 1 for any sleeping rate in any vertex-transitive graph in which simple random walk has positive speed. Furthermore, we prove that μc > 0 in any vertex-transitive amenable graph, and that μ c ∞ (0, 1) for any sleeping rate on regular trees. </p
Uniformly positive correlations in the Dimer model and macroscopic interacting self-avoiding walk in Zd, d≥3
Full text linkOur first main result is that correlations between monomers in the dimer model in (Formula presented.) do not decay to 0 when (Formula presented.). This is the first rigorous result about correlations in the dimer model in dimensions greater than 2 and shows that the model behaves drastically differently than in two dimensions, in which case it is integrable and correlations are known to decay to zero polynomially. Such a result is implied by our more general, second main result, which states the occurrence of a phase transition in the model of lattice permutations, which is related to the quantum Bose gas. More precisely, we consider a self-avoiding walk interacting with lattice permutations and we prove that, in the regime of fully packed loops, such a walk is ‘long’ and the distance between its endpoints grows linearly with the diameter of the box. These results follow from the derivation of a version of the infrared bound from a new general probabilistic settings, with coloured loops and walks interacting at sites and walks entering into the system from some ‘virtual’ vertices. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC
Critical probabilities and convergence time of Percolation Probabilistic Cellular Automata
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Exponential decay of transverse correlations for O(N) spin systems and related models
Full text linkWe 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 result is new when N>3, in which case no Lee–Yang theorem is available, it is an alternative to Lee–Yang when N=2,3, and also holds for a wide class of multi-component spin systems with continuous symmetry. The key ingredients are a representation of the model as a system of coloured random paths, a ‘colour-switch’ lemma, and a sampling procedure which allows us to bound from above the ‘typical’ length of the open paths
Site monotonicity and uniform positivity for interacting random walks and the spin O(N) model with arbitrary N
Full text linkWe provide a uniformly-positive point-wise lower bound for the two-point function of the classical spin O(N) model on the torus of ℤ^푑, 푑≥3, when 푁∈ℕ>0 and the inverse temperature 훽 is large enough. This is a new result when 푁>2 and extends the classical result of Fröhlich et al. (Commun Math Phys 50:79–95, 1976). Our bound follows from a new site-monotonicity property of the two-point function which is of independent interest and holds not only for the spin O(N) model with arbitrary 푁∈ℕ>0, but for a wide class of systems of interacting random walks and loops, including the loop O(N) model, random lattice permutations, the dimer model, the double-dimer model, and the loop representation of the classical spin O(N) model
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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