Comprehending Large Numbers

Making estimates is an excellent way to put numbers into perspective．For example,what does the number 1 million really mean? Our next example may help you to comprehend this large number．     

Large Cells in Poisson–Delaunay Tessellations

It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex, given that the volume of the typical cell tends to infinity. This follows from an estimate for the probability that the typical cell deviates by a given amount from regularity, given that its volume is large. As a tool for the proof, a stability result for simplices is established.     

Large Sets and Overlarge Sets of Triangle-Decomposition

There are six types of triangles:undirected triangle,cyclic triangle,transitive triangle,mixed-1triangle,mixed-2 triangle and mixed-3 triangle.The triangle-decompositions for the six types of triangles havealready been solved.For the first three types of triangles,their large sets have already been solved,and theiroverlarge sets have been investigated.In this paper,we establish the spectrum of LT_i(v,λ),OLT_i(v)(i=1,2),and give the existence of LT_3(v,λ)and OLT_3(v,λ)with λ even.     

Large time behavior of Euler-Poisson system for semiconductor

In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions converges to the stationary solutions exponentially in time.No smallness and regularity conditions are assumed.     

On the Self-Normalized Cramér-type Large Deviation

For the self-normalized sum, , it is shown that converges to 1, uniformly in a region, under the optimal assumption that the sampled distribution is in the domain of attraction of the normal law. Bounds for this convergence are given and their applications to exponential non-uniform Berry–Esseen bound are also discussed.     

Large deviation of some infinite-dimensional markov processes ∗

In this paper it is shown that a large deviation principle in the sense of Donsker and Varadhan is satisfied by the Ornstein-Uhlenbeck process on C[0,1].     

Moderately Large Deviations for Uniformly Ergodic Markov Processes

Let (Ω,P_x) be a Markov process with values in the Polish space Eand with transition kernel π(x,dy). Let μ be an invariant probability measure of πsuch that lim sup||π~n-μ||_(var)= 0 and a(n) be a sequence of positive real numbersn→∞X∈Esuch that a(n)/n(1/2)→∞, a(n)/n→0 as n→∞.We denote Ly L_n(w) the measure     

Large deviations for Glauber dynamics of continuous gas

This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems.We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology,while it does not satisfy the large deviation principles in the T-topology.     

Large entropy measures for endomorphisms of ℂℙ k

Let f be a holomorphic endomorphism of ?? ^k . We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large metric entropy, close to log d ^k . We establish for them strong stochastic properties and prove the positivity of their Lyapunov exponents. Since they have large entropy, those measures are supported in the support of the maximal entropy measure of f. They in particular provide lower bounds for the Hausdorff dimension of the Julia set.     

Refined Self-normalized Large Deviations for Independent Random Variables

Let X ₁,X ₂,…?, be independent random variables with EX _i =0 and write \(S_{n}=\sum_{i=1}^{n}X_{i}\) and \(V_{n}^{2}=\sum_{i=1}^{n}X_{i}^{2}\). This paper provides new refined results on the Cramér-type large deviation for the so-called self-normalized sum S _n /V _n . The major techniques used to derive these new findings are different from those used previously.     

Large deviations viewpoints for a heavy-tailed β-mixing sequence

Let {Xn; n ≥ 1} be a stationary sequenceof non-negative random variables with heavy tails. Under mixing conditions, we study logarithmic asymptotics for the disp(Sn ＞ nx) ≈ n-αx+1 for appropriate values of x, where α is a specific parameter. The related conjecture proposed by Gantert is investigated. As a by-product, the so-called supremum large deviations principle is also studied.     

Large deviations viewpoints for a heavy-tailed β-mixing sequence

Let (Xn;n≥1) be a stationary sequence of non-negative random variables with heavy tails. Under mixing conditions, we study logarithmic asymptotics for the distributions of the partial sums sn=X1 X2 … Xn. We obtain the crude estimates P(Sn>nx)≈n-αx 1 for appropriate values of x, where a is a specific parameter. The related conjecture proposed by Gantert is investigated. As a by-product, the so-called supremum large deviations principle is also studied.     

Global Optimization Using Diffusion Perturbations with Large Noise Intensity

This work develops an algorithm for global optimization.The algorithm is of gradient ascent typeand uses random perturbations.In contrast to the annealing type procedurcs,the perturbation noise intensityis large.We demonstrate that by properly varying the noise intensity,approximations to the global maximumcan be achieved.We also show that the expected time to reach the domain of attraction of the global maximum,which can be approximated by the solution of a boundary value problem,is finite.Discrete-time algorithmsare proposed;recursive algorithms with occasional perturbations involving large noise intensity are developed.Numerical examples are provided for illustration.     

Solving Large Sparse Linear and Quadratic Generalized Eigenvalue Problems

We study the methods for solving the following large order eigenvelue problems occurring in the analysis of structural vibration: (1) (2) and (3) where M and C are both symmetric matrices, while (?) is skew symmetric. Moreover, M is positive definite, and the matrix K in (2) and (3) is also assumed to be symmetric positive definite. 1 The eigenvalue problem for normal matrices in generalized inner prduct Let B be an n×n Hermitian positive definite matrix. Then     

Some perspective on the Large Scale Scientific Computation Research

The "Large Scale Scientific Computation (LSSC) Research" project is one of the State Major Basic Research projects funded by the Chinese Ministry of Science and Technology in the field of information science and technology. The LSSC research project is aimed at promoting basic research in large scale scientific computation in China through the development of innovative computational methods and software tools for grand challenge appli-     

Large Deviations for Two-Time-Scale Diffusions, with Delays

We consider the problem of large deviations for a two-time-scale reflected diffusion process, possibly with delays in the dynamical terms. The Dupuis-Ellis weak convergence approach is used. It is perhaps the most intuitive and simplest for the problems of concern. The results have applications to the problem of approximating optimal controls for two-time-scale systems via use of the averaged equation.     

Large Time Asymptotics for the BBM–Burgers Equation

We study large time asymptotics of solutions to the BBM–Burgers equation

Conditioning Galton–Watson Trees on Large Maximal Outdegree

We propose a new way to condition random trees, that is, conditioning random trees to have large maximal outdegree. Under this conditioning, we show that conditioned critical Galton–Watson trees converge locally to size-biased trees with a unique infinite spine. For the subcritical case, we obtain the local convergence to size-biased trees with a unique infinite node. We also study the tail of the maximal outdegree of subcritical Galton–Watson trees, which is essential for the proof of the local convergence.     

Large deviations for squared radial Ornstein–Uhlenbeck processes

In this paper, we state a large deviation principle (LDP) and sharp LDP for maximum likelihood estimators of drift coefficients of generalized squared radial Ornstein–Uhlenbeck processes. For that purpose, we present an LDP in a class of non-steep cases, where the Gärtner–Ellis theorem cannot be applied.