A triviality result in the AdS/CFT correspondence for Euclidean quantum fields with exponential interaction

We consider scalar quantum fields with exponential interaction on Euclidean hyperbolic space $\mathbb{H}^2$ in two dimensions. Using decoupling inequalities for Neumann boundary conditions on a tessellation of $\mathbb{H}^2$, we are able to show that the infra-red limit for the generating functional of the conformal boundary field becomes trivial.Comment: 13 pages, 1 figur

A noncommutative enumeration problem

In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of noncommutative formal power series.Comment: 14 pages, 3 figures, section 3 extende

The Feynman graph representation of convolution semigroups and its applications to L\'{e}vy statistics

We consider the Cauchy problem for a pseudo-differential operator which has a translation-invariant and analytic symbol. For a certain set of initial conditions, a formal solution is obtained by a perturbative expansion. The series so obtained can be re-expressed in terms of generalized Feynman graphs and Feynman rules. The logarithm of the solution can then be represented by a series containing only the connected Feynman graphs. Under some conditions, it is shown that the formal solution uniquely determines the real solution by means of Borel transforms. The formalism is then applied to probabilistic L\'{e}vy distributions. Here, the Gaussian part of such a distribution is re-interpreted as a initial condition and a large diffusion expansion for L\'{e}vy densities is obtained. It is outlined how this expansion can be used in statistical problems that involve L\'{e}vy distributions.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ106 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Central Limit Theorem for Coloured Hard Dimers

We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs. The techniques used at arriving this result comprise combinatorics, generating functions, and conditional expectations

AdS/CFT correspondence in the Euclidean context

We study two possible prescriptions for AdS/CFT correspondence by means of functional integrals. The considerations are non-perturbative and reveal certain divergencies which turn out to be harmless, in the sense that reflection-positivity and conformal invariance are not destroyed.Comment: 20 pages, references and two remarks adde

Risk assessment and prevention priorities in cultural heritage preservation

European Union has been promoting research actions on cultural heritage, recognizing and underlining its central role for the community policies and establishing its safeguard and valorisation as urgent priorities for the future. A research on rational tools for establishing seismic risk, intervention priorities, and decision-making on renovation of historical buildings and museums, just started at the University of Camerino, School of Architecture and Design, is described in this paper. The basic idea of the research is to develop a probabilistic methodology for the assessment of seismic risk of cultural Heritage starting from the Pacific Earthquake Engineering Research (PEER) approach, consisting of a general framework where the risk problem is decomposed into its three main features (i.e. seismic hazard, vulnerability and losses), analysed in a rigorous and consistent interdependent manner. The application of this methodology to cultural heritage requires investigations and original proposals on various open issues. This paper reports some results concerning the general methodology and preliminary analyses of a case study