1,720,971 research outputs found
Quantum Methods for Interacting Particle Systems II, Glauber Dynamics for Ising Spin Systems
No full textUsing the formalism and the results described in [QMPS I] and in
[QMPS III], we discuss the approach to termodynamic equilibrium for discrete
spin systems in a framework that generalizes the one originally proposed by
R. Glauber. Ergodicity for the process is proved by providing a lower bound
extimate for their exponetial rate of convergence to equilibrium, in the high
temperature regime. We give application to some (not necessarily ferromagnetic ) Ising-spin models. These results also gives an upper bound for the
critical temperature of the d-dimensional Ising model, which in dimension two
coincides with the real critical value calculated by the static approach
Speed of Parallel Processing for Random Task Graphs
No full textThe random graph model of parallel computation introduced by Gelenbe et al. depends on three
parameters: n, the number of tasks (vertices); F, the common distribution of Ti,. . . , T,, the task
processing times, and p = p,, the probability for a given i < j that task i must be completed before
task j is started. The total processing time is R,,, the maximum sum of T,’s along directed paths of
the graph. We study the large n behavior of Rn when np,, grows sublinearly but superlogarithmically,
the regime where the longest directed path contains about enp,, tasks. For an exponential (mean one)
F, we prove that R,, is about 4np,. The “discrepancy” between 4 and e is a large deviation effect.
Related results are obtained when np,, grows exactly logarithmically and when F is not exponential,
but has a tail which decays (at least) exponentially fast
Analyticity of the Density and Exponential Decay of Correlations in 2-d Bootstrap Percolation
No full textOn some features of quadratic unconstrained binary optimization with random coefficients
No full textQuadratic Unconstrained Binary Optimization (QUBO or UBQP) is concerned with maximizing/minimizing the quadratic form H(J,eta)=W & sum;(i,j)J(i,j)eta(i)eta(j )with J a matrix of coefficients, eta is an element of {0,1}(N) and W a normalizing constant. In the statistical mechanics literature, QUBO is a lattice gas counterpart to the (generalized) Sherrington-Kirkpatrick spin glass model. Finding the optima of H is an NP-hard problem. Several problems in combinatorial optimization and data analysis can be mapped to QUBO in a straightforward manner. In the combinatorial optimization literature, random instances of QUBO are often used to test the effectiveness of heuristic algorithms. Here we consider QUBO with random independent coefficients and show that if the J(i,j)'s have zero mean and finite variance then, after proper normalization, the minimum and maximum per particle of H do not depend on the details of the distribution of the couplings and are concentrated around their expected values. Further, with the help of numerical simulations, we study the minimum and maximum of the objective function and provide some insight into the structure of the minimizer and the maximizer of H. We argue that also this structure is rather robust. Our findings hold also in the diluted case where each of the J(i,j)'s is allowed to be zero with probability going to 1 as N ->infinity in a suitable way
Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension
No full text
On the Implications of the OFF Period Distribution in two-State Traffic Models
No full textThe goal of the letter is to highlight the impact of the
inactive period distribution of an ON–OFF source on the autocor relation structure of the model. In particular, two discrete-time
ON–OFF models, both with geometric distribution of the active
period, are considered: the GeoGeo Model (GGM) and the
ParetoGeo Model (PGM), characterized by a geometric and
Pareto-like distribution of the OFF periods length, respectively.
The two models are compared in terms of their main statistical
features as well as queueing impact. The asymptotic behavior
of the autocorrelation function for the proposed PGM has been
analytically evaluated. It is shown it has a hyperbolic decay
related to the tail behavior of the OFF periods distribution
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