1,720,964 research outputs found
On the spectral gap of some Cayley graphs on the Weyl group W(Bn)
Full text linkThe Laplacian of a (weighted) Cayley graph on the Weyl group W(Bn) is a N×N matrix with N=2nn! equal to the order of the group. We show that for a class of (weighted) generating sets, its spectral gap (lowest nontrivial eigenvalue), is actually equal to the spectral gap of a 2n×2n matrix associated to a 2n-dimensional permutation representation of Wn. This result can be viewed as an extension to W(Bn) of an analogous result valid for the symmetric group, known as “Aldous' spectral gap conjecture”, proven in 2010 by Caputo, Liggett and Richthammer
On the layering transition of an SOS surface interacting with a wall .2. The Glauber dynamics
No full textThe spectral gap for a Glauber-type dynamics in a continuous gas
No full textWe consider a continuous gas in a d-dimensional rectangular box with a
finite range, positive pair potential, and we construct a Markov process
in which particles appear and disappear with appropriate rates so that
the process is reversible w.r.t. the Gibbs measure. If the
thermodynamical paramenters are such that the Gibbs specification
satisfies a certain mixing condition, then the spectral gap of the
generator is strictly positive uniformly in the volume and boundary
condition. The required mixing condition holds if, for instance, there
is a convergent cluster expansion
The spectral gap for the Kawasaki dynamics at low temperature
No full textIn this paper we analyze the convergence to equilibrium of Kawasaki dynamics for the Ising model in the phase coexistence region. First we show, in strict analogy. with the nonconservative case, that in any lattice dimension, for any boundary condition and any positive temperature and particle density, the spectral gap in a box of side L does not shrink faster than a negative exponential of the surface Ld-1. Then we prove that, in two dimensions and for free boundary condition, the spectral gap in a box of side L is smaller than a negative exponential of L provided that the temperature is below the critical one and the particle density rho satisfies p is an element of (p(-)*, p(+)*), where p(+/-)* represents the particle density of the plus and minus phase, respectively
On the layering transition of an SOS surface interacting with a wall .1. Equilibrium results
No full textWe consider the model of a 2D surface above a fixed wall and attracted toward it by means of a positive magnetic field h in the solid-on-solid (SOS) approximation when the inverse temperature beta is very large and the external field h is exponentially small in beta. We improve considerably previous results by Dinaburg and Mazel on the competition between the external field and the entropic repulsion with the wall, leading, in this case, to the phenomenon of layering phase transitions. In particular, we show, using the Pirogov-Sinai scheme as given by Zahradnik, that there exists a unique critical value h*(k)(beta) in the interval (1/4e(-4 beta k), 4e(-4 beta k)) such that, for all h is an element of (h*(k+1), h*(k)) and beta large enough, there exists a unique infinite-volume Gibbs state. The typical configurations are small perturbations of the ground state represented by a surface at height k+1 above the wall. Moreover, for the same choice of the thermodynamic parameters, the influence of the boundary conditions of the Gibbs measure in a finite cube decays exponentially fast with the distance from the boundary. When h=h*(k)(beta) we prove instead the convergence of the cluster expansion for both k and k+1 boundary conditions. This fact signals the presence of a phase transition. In the second paper of this series we will consider a Glauber dynamics for the above model and we will study the rate of approach to equilibrium in a large finite cube with arbitrary boundary conditions as a function of the external field ii. Using the results proven in this paper, we will show that there is a dramatic slowing down in the approach to equilibrium when the magnetic field takes one of the critical values and the boundary conditions are free (absent)
On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point
No full text
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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