The role of disorder in the dynamics of critical fluctuations of mean field models

The purpose of this paper is to analyze how the disorder affects the dynamics of critical fluctuations for two different types of interacting particle system: the Curie-Weiss and Kuramoto model. The models under consideration are a collection of spins and rotators respectively. They both are subject to a mean field interaction and embedded in a site-dependent, i.i.d. random environment. As the number of particles goes to infinity their limiting dynamics become deterministic and exhibit phase transition. The main result concern the fluctuations around this deterministic limit at the critical point in the thermodynamic limit. From a qualitative point of view, it indicates that when disorder is added spin and rotator systems belong to two different classes of universality, which is not the case for the homogeneous models (i.e., without disorder).Comment: 41 page

Logarithmic Sobolev Inequality for Zero-Range Dynamics: independence of the number of particles

We prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter L may depend on L but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as L^2, that will be presented in a forthcoming paper

Logarithmic Sobolev inequality for zero-range Dynamics

We prove that the logarithmic Sobolev constant for zero-range processes in a box of diameter $L$ grows as $L^2$.Comment: Published at http://dx.doi.org/10.1214/009117905000000332 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hitting times for special patterns in the symmetric exclusion process on Z^d

We consider the symmetric exclusion process {\eta_t,t>0} on {0,1}^{Z^d}. We fix a pattern A:={\eta:\sum_{\Lambda}\eta(i)\ge k}, where \Lambda is a finite subset of Z^d and k is an integer, and we consider the problem of establishing sharp estimates for \tau, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for \tau in a simple way. Also, we characterize the trajectories {\eta_s,s\le t} conditioned on {\tau>t}.Comment: Published at http://dx.doi.org/10.1214/009117904000000487 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multi-scaling of moments in stochastic volatility models

We introduce a class of stochastic volatility models $(X_t)_{t \geq 0}$ for which the absolute moments of the increments exhibit anomalous scaling: \E\left(|X_{t+h} - X_t|^q \right) scales as $h^{q/2}$ for $q < q^*$, but as $h^{A(q)}$ with $A(q) q^*$, for some threshold $q^*$. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driven by a Levy subordinator and the characteristic measure of the Levy process has power law tails, then multi-scaling occurs if and only if the mean reversion is superlinear

The dynamics of critical fluctuations in asymmetric Curie-Weiss models

We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie-Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit reflect the type of bifurcation, as they exhibit observables whose fluctuations evolve at different time scales. The limiting dynamics of fluctuations of slow observable is obtained via an averaging principle.Comment: 27 page

Consumption of wood biomass in Italy: a strategic role based on a weak knowledge

Given the growing role of wood biomass as a strategic resource in the European and national renewable energy policies, the paper provides two new estimations of the internal consumption and supply levels, aiming at discussing the real role of this resource in the national energy mix and the implications of this market in terms of forest policies. The first estimation focuses on household consumption and expenditure based on the ISTAT \u201cSurvey on consumption by families\u201d, and the second analyzes how the wood biomass supply is structured and organized; this second estimation has been carried out with an expert panel consultation based on a Delphi-based approach. These two estimations are then compared and discussed with reference to the data and information provided by official sources and other publically-available studies and surveys conducted in recent years. The results provide evidence that wood biomass is the first source of renewable energy in Italy and that official data only partially quantify the consumption levels in the residential sector and domestic supply rates. The paper highlights the need for a new approach in data collection on this fast-growing market; these data are essential for a more effective implementation of the renewable energy policy and other relevant forest-related policies such as those on climate and wood mobilization

Meyniel's conjecture holds for random graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph $G$ is called the cop number of $G$. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant $C$, the cop number of every connected graph $G$ is at most $C \sqrt{|V(G)|}$. In this paper, we show that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. We do this by first showing that the conjecture holds for a general class of graphs with some specific expansion-type properties. This will also be used in a separate paper on random $d$-regular graphs, where we show that the conjecture holds asymptotically almost surely when $d = d(n) \ge 3$.Comment: revised versio