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We study the so-called nonconventional averages in the context of lattice spin systems, or equivalently random colourings of the integers. For i.i.d. colourings, we prove a large deviation principle for the number of monochromatic arithmetic progress
Externí odkaz:
http://arxiv.org/abs/1110.2354
We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other
Externí odkaz:
http://arxiv.org/abs/0906.4664
Publikováno v:
Annals of Applied Probability 2009, Vol. 19, No. 4, 1581-1602
We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based
Externí odkaz:
http://arxiv.org/abs/0708.2165
We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the covariance of the energy exhibits long-range correl
Externí odkaz:
http://arxiv.org/abs/cond-mat/0612198
Autor:
Contucci, P., Giardina', C.
We comment on recent numerical experiments by G.Hed and E.Domany [cond-mat/0608535v2] on the quenched equilibrium state of the Edwards-Anderson spin glass model. The rigorous proof of overlap identities related to replica equivalence shows that the o
Externí odkaz:
http://arxiv.org/abs/cond-mat/0611138
Publikováno v:
Phys. Rev. Lett. 99, 057206 (2007)
We test the property of ultrametricity for the spin glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to $20^3$ spins. We find an excellent agreement with the prediction of the mean field theory. Sinc
Externí odkaz:
http://arxiv.org/abs/cond-mat/0607376
Autor:
Giardina', C., Kurchan, J.
We introduce a family of Hamiltonian models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases Fourier law is verified in one di
Externí odkaz:
http://arxiv.org/abs/cond-mat/0502485
Autor:
Contucci, P., Giardina', C.
We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-average for both the She
Externí odkaz:
http://arxiv.org/abs/math-ph/0408002
We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a $d$-dimensional lattice, including spin glasses. We develop a method which relies simply
Externí odkaz:
http://arxiv.org/abs/cond-mat/0401211