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In this short note we present an alternative proof of the so-called First Visit Time Lemma (FVTL), originally presented by Cooper and Frieze in its first formulation in [21], and then used and refined in a list of papers by Cooper, Frieze and coauthors. We work in the original setting, considering a growing sequence of irreducible Markov chains on $n$ states. We assume that the chain is rapidly mixing and with a stationary measure having no entry which is too small nor too large. Under these assumptions, the FVTL shows the exponential decay of the distribution of the hitting time of a given state $x$ -- for the chain started at stationarity -- up to a small multiplicative correction. While the proof of the FVTL presented by Cooper and Frieze is based on tools from complex analysis, and it requires an additional assumption on a generating function, we present a completely probabilistic proof, relying on the theory of quasi-stationary distributions and on strong-stationary times arguments. In addition, under the same set of assumptions, we provide some quantitative control on the Doob's transform of the chain on the complement of the state $x$.

Considering the complexity of controller systems in and also managing a microgrid (MGs), using automation systems can be an effective step in increasing energy efficiency, high reliability, as well as economic and environmental issues. In order to achieve these goals, this paper presents a comprehensive testbed for control and energy management in MG lab project is called LAMBDA MG in Sapienza University of Rome. The MG is composed of several sources (Photovoltaic, Storage, Emergency Generator Set) a smart switchboard and loads (lights, HVAC, plugs). The control strategy consists of two different subnets: the first one is based on a distributed home and building electronic system (HBES) for the supervisory and control for energy and comfort goals and the second one based on a central PLC for the operation of the different sources in grid and island mode respect the grid. The two subnets are integrated in a common SCADA system able to provide a real time monitoring, alarm handling, human machine interfacing, event and data.

Currently, despite the use of renewable energy sources (RESs), distribution networks are facing problems, such as complexity and low productivity. Emerging microgrids (MGs) with RESs based on supervisory control and data acquisition (SCADA) are an effective solution to control, manage, and finally deal with these challenges. The development and success of MGs is highly dependent on the use of power electronic interfaces. The use of these interfaces is directly related to the progress of SCADA systems and communication infrastructures. The use of SCADA systems for the control and operation of MGs and active distribution networks promotes productivity and efficiency. This paper presents a real MG case study called the LAMBDA MG testbed laboratory, which has been implemented in the electrical department of the Sapienza University of Rome with a centralized energy management system (CEMS). The real-time results of the SCADA system show that a CEMS can create proper energy balance in a LAMBDA MG testbed and, consequently, minimize the exchange power of the LAMBDA MG and main grid.

We analyze the relaxation time of a ferromagnetic d-dimensional growth model on the lattice. The model is characterized by d parameters which represent the activation energies of a site, depending on the number of occupied nearest neighbours. This model is a natural generalisation of the model studied by Dehghanpour and Schonmann (Probab Theory Relat Fields. 107(1):123–135, 1997), where the activation energy of a site with more than two occupied neighbours is zero.

We prove that the threshold regime for bootstrap percolation in a d -dimensional box of diameter L with parameters p and l, where 3⩽l⩽ d , is L∼ exp ° (l−1) (Cp −1/(d−l+1) ) , where exp° (l−1) is the exponential iterated l−1 times and C is bounded from above and from below by two positive constants depending on d , l only.

We consider Glauber dynamics of classical spin systems of Ising type in the limit when the temperature tends to zero in finite volume. We show that information on the structure of the most profound minima and the connecting saddle points of the Hamiltonian can be translated into sharp estimates on the distribution of the times of metastable transitions between such minima as well as the low lying spectrum of the generator. In contrast with earlier results on such problems, where only the asymptotics of the exponential rates is obtained, we compute the precise pre-factors up to multiplicative errors that tend to 1 as T↓0. As an example we treat the nearest neighbor Ising model on the 2 and 3 dimensional square lattice. Our results improve considerably earlier estimates obtained by Neves–Schonmann,(1) Ben Arous–Cerf,(2) and Alonso–Cerf.(3) Our results employ the methods introduced by Bovier, Eckhoff, Gayrard, and Klein in refs. 4 and 5.

This work extends to dimension $d\geq3$ the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on ${\mathbb{Z}}^d$ evolving with the Metropolis dynamics under a fixed small positive magnetic field $h$ starting from the minus phase. When the inverse temperature $\beta$ goes to $\infty$, the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like $\exp({{\beta}{\kappa}_d})$. The value $\kappa_d$ is equal to \[{\kappa}_d=\frac{1}{d+1}({\Gamma}_1+\cdots+{\Gamma}_d),\] where ${\Gamma}_i$ is the energy of the $i$-dimensional critical droplet of the Ising model at zero temperature and magnetic field $h$., Comment: Published in at http://dx.doi.org/10.1214/12-AOP801 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We consider a Hamiltonian system given by a charged particle under the action of a constant electric field and interacting with a medium, which is described as a Vlasov fluid. We assume that the action of the charged particle on the fluid is negligible and that the latter has one-dimensional symmetry. We prove that if the singularity of the particle/medium interaction is integrable and the electric field intensity is large enough, then the particle escapes to infinity with a quasi-uniformly accelerated motion. A key tool in the proof is a new estimate on the growth in time of the fluid particle velocity for one-dimensional Vlasov fluids with bounded interactions.