Related papers: Two Groups in a Curie-Weiss Model
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We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these…
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In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site…
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The Standard Model of particle physics may seem complicated and arbitrary, but it has hidden patterns that are revealed by the relationship between three "grand unified theories": theories that unify forces and particles by extending the…
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Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
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A uniform law of large numbers and a central limit theorem are established via a martingale approach for a univariate Hawkes process with immigration given by a renewal process. The results are obtained for renewal processes with absolutely…
The renormalization-group method is used to analyze the low-temperature behaviour of a two-dimentional, spin-$s$ quantum Heisenberg ferromagnet. A set of recursion equations is derived in an one-loop approximation. The low-temperature…
Using numerical Real Space Renormalisation Group methods as well as Stochastic Series Expansions Quantum Monte Carlo simulations a generic model of diluted spin-1/2 impurities interacting at long distances is investigated. Such a model…