Abstract:
We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and $n$ objects spatially uniformly distributed, each object being allocated to a bin at a cost depending on its position. Two allocations are considered: the allocation minimizing the bin loads and the allocation allocating each object to its less costly bin. We analyze the asymptotic properties of these allocations as the number of objects grows to infinity. Using the symmetries of the problem, we derive a law of large numbers, a central limit theorem and a large deviation principle for both loads with explicit expressions. In particular, we prove that the two allocations satisfy the same law of large numbers, but they do not have the same asymptotic fluctuations and rate functions.

Abstract:
In this paper we prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes.

Abstract:
Under different assumptions on the distribution of the fading random variables, we derive large deviation estimates for the tail of the interference in a wireless network model whose nodes are placed, over a bounded region of the plane, according to the $\beta$-Ginibre process, $0<\beta\leq 1$. The family of $\beta$-Ginibre processes is formed by determinantal point processes, with different degree of repulsiveness, which converge in law to a homogeneous Poisson process, as $\beta \to 0$. In this sense the Poisson network model may be considered as the limiting uncorrelated case of the $\beta$-Ginibre network model. Our results indicate the existence of two different regimes. When the fading random variables are bounded or Weibull superexponential, large values of the interference are typically originated by the sum of several equivalent interfering contributions due to nodes in the vicinity of the receiver. In this case, the tail of the interference has, on the log-scale, the same asymptotic behavior for any value of $0<\beta\le 1$, but it differs (again on a log-scale) from the asymptotic behavior of the tail of the interference in the Poisson network model. When the fading random variables are exponential or subexponential, instead, large values of the interference are typically originated by a single dominating interferer node and, on the log-scale, the asymptotic behavior of the tail of the interference is essentially insensitive to the distribution of the nodes. As a consequence, on the log-scale, the asymptotic behavior of the tail of the interference in any $\beta$-Ginibre network model, $0<\beta\le 1$, is the same as in the Poisson network model.

Abstract:
In this paper we analyze Least Recently Used (LRU) caches operating under the Shot Noise requests Model (SNM). The SNM was recently proposed to better capture the main characteristics of today Video on Demand (VoD) traffic. We investigate the validity of Che's approximation through an asymptotic analysis of the cache eviction time. In particular, we provide a large deviation principle, a law of large numbers and a central limit theorem for the cache eviction time, as the cache size grows large. Finally, we derive upper and lower bounds for the "hit" probability in tandem networks of caches under Che's approximation.

Abstract:
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and admits the distribution of the determinantal process as reversible law. In particular, this approach allows us to build a concrete example of the associated diffusion process, providing an illustration of the results of [4] and [30].

Abstract:
The study of surface morphology of Au deposited on mica is crucial for the fabrication of flat Au films for applications in biological, electronic, and optical devices. The understanding of the growth mechanisms of Au on mica allows to tune the process parameters to obtain ultra-flat film as suitable platform for anchoring self-assembling monolayers, molecules, nanotubes, and nanoparticles. Furthermore, atomically flat Au substrates are ideal for imaging adsorbate layers using scanning probe microscopy techniques. The control of these mechanisms is a prerequisite for control of the film nano- and micro-structure to obtain materials with desired morphological properties. We report on an atomic force microscopy (AFM) study of the morphology evolution of Au film deposited on mica by room-temperature sputtering as a function of subsequent annealing processes. Starting from an Au continuous film on the mica substrate, the AFM technique allowed us to observe nucleation and growth of Au clusters when annealing process is performed in the 573-773 K temperature range and 900-3600 s time range. The evolution of the clusters size was quantified allowing us to evaluate the growth exponent 〈z〉 = 1.88 ± 0.06. Furthermore, we observed that the late stage of cluster growth is accompanied by the formation of circular depletion zones around the largest clusters. From the quantification of the evolution of the size of these zones, the Au surface diffusion coefficient was evaluated in D ( T ) = [ ( 7 . 42 × 1 0 13 ) ± ( 5 . 94 × 1 0 14 ) m 2 /s ] exp ( ( 0.33 ± 0.04 ) eV k T ) . These quantitative data and their correlation with existing theoretical models elucidate the kinetic growth mechanisms of the sputtered Au on mica. As a consequence we acquired a methodology to control the morphological characteristics of the Au film simply controlling the annealing temperature and time.

Abstract:
Television is attracting an enormous amount of attention from both researchers and managers, due to the profound changes that are taking place thanks to the diffusion of digital technology. The study of the digital landscape of television, including the players competing in its arena and their strategies, is well worth the effort. This paper, based on 32 case studies and the census of the Sofa-TV (Sat TV, DTT, and IPTV) offerings, aims at describing the current state of channel offerings, individualizing the principal players, and identifying their strategies, thus allowing us to give a few predictions as to the possible future changes in the industry. The analysis will have a general applicability, as the considerations made are not particularly country-specific, although performed within the Italian context, one of the most advanced in the development of digital television platforms.

Abstract:
The real coordinates separating geodesic Hamilton-Jacobi equation on three-dimensional Minkowski space in several cases cannot be defined in the whole space. We show through an example how to naturally extend them to complex variables defined everywhere (excluding the singular surfaces of each coordinate system only) and still separating the same equation.

Abstract:
We investigate an attractive atomic Bose-Einstein condensate (BEC) trapped by a double-well potential in the axial direction and by a harmonic potential in the transverse directions. We obtain numerically, for the first time, a quantum phase diagram which includes all the three relevant phases of the system: Josephson, spontaneous symmetry breaking (SSB), and collapse. We consider also the coherent dynamics of the BEC and calculate the frequency of population-imbalance mode in the Josephson phase and in the SSB phase up to the collapse. We show that these phases can be observed by using ultracold vapors of 7Li atoms in a magneto-optical trap.

Abstract:
In this paper the geometric theory of separation of variables for time-independent Hamilton-Jacobi equation is extended to include the case of complex eigenvalues of a Killing tensor on pseudo-Riemannian manifolds. This task is performed without to complexify the manifold but just considering complex-valued functions on it. The simple formalism introduced allows to extend in a very natural way the classical results on separation of variables (including Levi-Civita criterion and Stackel-Eisenhart theory) to the complex case. Orthogonal variables only are considered.