On the dynamics of trap models in Z^d

We consider trap models on Z^d, namely continuous time Markov jump process on Z^d with embedded chain given by a generic discrete time random walk, and whose mean waiting time at x is given by tau_x, with tau = (tau_x, x in Z^d) a family of positive iid random variables in the basin of attraction of an alpha-stable law, 0<alpha<1. We may think of x as a trap, and tau_x as the depth of the trap at x. We are interested in the trap process, namely the process that associates to time t the depth of the currently visited trap. Our first result is the convergence of the law of that process under suitable scaling. The limit process is given by the jumps of a certain alpha-stable subordinator at the inverse of another alpha-stable subordinator, correlated with the first subordinator. For that result, the requirements for the embedded random walk are a) the validity of a law of large numbers for its range, and b) the slow variation at infinity of the tail of the distribution of its time of return to the origin: they include all transient random walks as well as all planar random walks, and also many one dimensional random walks. We then derive aging results for the process, namely scaling limits for some two-time correlation functions thereof, a strong form of which requires an assumption of transience, stronger than a, b. The above mentioned scaling limit result is an averaged result with respect to tau. Under an additional condition on the size of the intersection of the ranges of two independent copies of the embeddded random walk, roughly saying that it is small compared with the size of the range, we derive a stronger scaling limit result, roughly stating that it holds in probability with respect to tau. With that additional condition, we also strengthen the aging results, from the averaged version mentioned above, to convergence in probability with respect to tau.Comment: 36 pages, 5 figures. Replaces first version, with a correction to/weakening of the statement of current Theorem 25, corrections to its proof and that of Lemma 16, the addition of a subsection on integrated aging results. Section 4, on convergence, was somewhat restructure

Economia política da Arte Moderna II / notas para uma sistematização provisória

Paradigma tradicional de excelência artesanal, com que meios pode a pintura responder à abstração do trabalho e à sua ordenação serial, inerentes à modernização capitalista? O texto presente busca sistematizar os momentos decisivos de um percurso que se estende de Manet (1832-1883) a Rothko (1903-1970). Constitui o capítulo conclusivo de uma investigação sobre a transformação crítica do modo de pintar em modo de fabricação, fundado na superação reflexiva da dicotomia entre trabalho intelectual e corporal, imposta historicamente à sociedade. Atualizada criticamente e assinalando um fecho possível do processo da arte moderna, a pintura de Rothko põe-se como a negação de todo aspecto individual da pintura e de unidade orgânica e monádica da obra. Alcança-se assim o último termo de um processo; termo que assinala o fim do ciclo da autonomia estética como forma ligada à liberdade do sujeito, idealizado como natureza desinteressada. Para o trabalho de resistência contra a aceleração da barbárie é fundamental doravante levar em conta os fatores de heteronomia supraindividuais que, se não logram controlar toda a produção, detêm a hegemonia na esfera da circulação.Traditional paradigm of craftsmanship excellence, how could painting answer to the process of labour abstraction and to serial production, inherent to capitalistic modernization? vvThe text seeks to systematize the decisive moments of the journey that extends from Manet (1832-1883) to Rothko (1903-1970). It constitutes the conclusive chapter of an inquiry on the critical transformation of a mode of painting, founded on the reflexive overcoming of the dichotomy between intellectual and manual work, historically imposed on society. Updated critically and designating a possible closing to the process of modern art, Rothko's painting sets itself as the negation of painting's individual aspects and of the organic and monadic unity of the work. The last term of a process is so reached; term that indicates the end of aesthetical autonomy cycle as a form linked to subject's freedom, idealized as disinterested nature. For the work of resistance against acceleration of barbarism is henceforth fundamental to take into account the supra-individual heteronomy factors that, if they do not manage to control the whole production process, indeed keep hegemony in the sphere of circulation