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1.
We consider systems of spatially distributed branching particles in R d . The particle lifelengths are of general form, hence the time propagation of the system is typically not Markov. A natural time-space-mass scaling is applied to a sequence of particle systems and we derive limit results for the corresponding sequence of measure-valued processes. The limit is identified as the projection on R d of a superprocess in R +×R d . The additive functional characterizing the superprocess is the scaling limit of certain point processes, which count generations along a line of descent for the branching particles.  相似文献   

2.
We extend results on time-rescaled occupation time fluctuation limits of the (d, α, β)-branching particle system (0 < α ≤ 2, 0 < β ≤ 1) with Poisson initial condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial intensity measure) were obtained for dimensions d > α / β only, since the particle system becomes locally extinct if dα / β. In this paper we show that by introducing high density of the initial Poisson configuration, limits are obtained for all dimensions, and they coincide with the previous ones if d > α / β. We also give high-density limits for the systems with finite intensity measures (without high density no limits exist in this case due to extinction); the results are different and harder to obtain due to the non-invariance of the measure for the particle motion. In both cases, i.e., Lebesgue and finite intensity measures, for low dimensions [d < α (1 + β) / β and d < α (2 + β) / (1 + β), respectively] the limits are determined by non-Lévy self-similar stable processes. For the corresponding high dimensions the limits are qualitatively different: -valued Lévy processes in the Lebesgue case, stable processes constant in time on (0,∞) in the finite measure case. For high dimensions, the laws of all limit processes are expressed in terms of Riesz potentials. If β = 1, the limits are Gaussian. Limits are also given for particle systems without branching, which yields in particular weighted fractional Brownian motions in low dimensions. The results are obtained in the setup of weak convergence of -valued processes. Research supported by MNiSW grant 1P03A1129 (Poland; T. Bojdecki and A. Talarczyk) and by CONACyT grant 45684-F (Mexico; L.G. Gorostiza).  相似文献   

3.
We consider a conservative stochastic lattice-gas dynamics reversible with respect to the canonical Gibbs measure of the bond dilute Ising model on ℤ d at inverse temperature β. When the bond dilution density p is below the percolation threshold we prove that for any particle density and any β, with probability one, the spectral gap of the generator of the dyamics in a box of side L centered at the origin scales like L −2. Such an estimate is then used to prove a decay to equilibrium for local functions of the form where ε is positive and arbitrarily small and α = ? for d = 1, α=1 for d≥2. In particular our result shows that, contrary to what happes for the Glauber dynamics, there is no dynamical phase transition when β crosses the critical value β c of the pure system. Received: 10 April 2000 / Revised version: 23 October 2000 / Published online: 5 June 2001  相似文献   

4.
We study the scaling limits of three different aggregation models on ℤ d : internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in ℝ d . In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.  相似文献   

5.
By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order two-point boundary value problem
is obtained under some conditions of growth, where α, β, γ, δ ≥ 0, ρ = αγ + γβ + δα > 0, and h(t) is allowed to be singular at t = 0 and t = 1. Supported by the National Natural Science Foundation of China(10771031,10671167).  相似文献   

6.
We establish an almost sure scaling limit theorem for super-Brownian motion on ℝ d associated with the semi-linear equation ut=\frac12Du+bu-au2u_{t}=\frac{1}{2}\Delta u+\beta u-\alpha u^{2} , where α and β are positive constants. In this case, the spectral theoretical assumptions required in Chen et al. (J. Funct. Anal. 254:1988–2019, 2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in ℝ d .  相似文献   

7.
Given non-negative integers l, m, n, α, β and γ with lα ≥ 1, mβ ≥ 1 and nγ ≥ 1, an [α,β,γ]-tripartite hypertournament on l + m + n vertices is a four tuple (U, V, W, E), where U, V and W are three sets of vertices with |U| = l , |V| = m and |W| = n, and E is a set of (α + β + γ)-tuples of vertices, called arcs, with exactly α vertices from U, exactly β vertices from V,and exactly γ vertices from W, such that any subset U1V1W1 of UVW, E contains exactly one of the (α + β + γ)! (α + β + γ) − tuples whose entries belong to U1V1W1. We obtain necessary and sufficient conditions for three lists of non-negative integers in non-decreasing order to be the losing score lists or score lists of some [α, β, γ]-tripartite hypertournament. Supported by National Science Foundation of China (No.10501021).  相似文献   

8.
In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф(r) = r^N-d/α (log log l/r)d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d, α) strictly stable processes.  相似文献   

9.
On weighted approximation by Bernstein-Durrmeyer operators   总被引:6,自引:0,他引:6  
In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals. Supported by Zhejiang Provincial Science Foundation.  相似文献   

10.
We study the percolative properties of random interlacements on G×ℤ, where G is a weighted graph satisfying certain sub-Gaussian estimates attached to the parameters α>1 and 2≤βα+1, describing the respective polynomial growths of the volume on G and of the time needed by the walk on G to move to a distance. We develop decoupling inequalities, which are a key tool in showing that the critical level u for the percolation of the vacant set of random interlacements is always finite in our set-up, and that it is positive when α≥1+β/2. We also obtain several stretched exponential controls both in the percolative and non-percolative phases of the model. Even in the case where G=ℤ d , d≥2, several of these results are new.  相似文献   

11.
LetT be the mod 1 circle group, α∈T be irrational and 0<β<1. LetE be the closed subgroup ofR generated by β and 1. DefineX=T×E andT:X→X byT(x, t)=(x+α,t+1 [0,β] (x)−β). Then we have the theorem:T is ergodic if and only if β is rational or 1, α and β are linearly independent over the rationals. This paper was prepared while I was very graciously hosted by the Centro de Investigacion y Estudios Avanzados, Mexico City.  相似文献   

12.
Ifα is an irreducible nonexpansive ergodic automorphism of a compact abelian groupX (such as an irreducible nonhyperbolic ergodic toral automorphism), thenα has no finite or infinite state Markov partitions, and there are no nontrivial continuous embeddings of Markov shifts inX. In spite of this we are able to construct a symbolic spaceV and a class of shift-invariant probability measures onV each of which corresponds to anα-invariant probability measure onX. Moreover, everyα-invariant probability measure onX arises essentially in this way. The last part of the paper deals with the connection between the two-sided beta-shiftV β arising from a Salem numberβ and the nonhyperbolic ergodic toral automorphismα arising from the companion matrix of the minimal polynomial ofβ, and establishes an entropy-preserving correspondence between a class of shift-invariant probability measures onV β and certainα-invariant probability measures onX. This correspondence is much weaker than, but still quite closely modelled on, the connection between the two-sided beta-shifts defined by Pisot numbers and the corresponding hyperbolic ergodic toral automorphisms.  相似文献   

13.
Summary In analogy with ordinary continuous Media [6], a intrinsical lagrangean formulation is given for the dynamics of hyperelastic Cosserat's oriented bodies. The 1o order Cauchy Problem, in terms of actuals variables:shifters d r α ,deformation rate kαβ andspin (constrained ωαβ andfree bαβ), insures the geometric-cinematic compatibility conditions for the metric gαβ and directorsd r.

A Dario Graffi nel suo 70° compleanno

Entrata in Redazione il 23 aprile 1975.  相似文献   

14.
In this paper, Tanaka formulae for (α, d, β)-superprocesses in the dimensions where the local time exists are established under the optimal initial condition.  相似文献   

15.
A theorem of Bourgain states that the harmonic measure for a domain in ℝ d is supported on a set of Hausdorff dimension strictly less thand [2]. We apply Bourgain’s method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of ℤ d ,d≥2. By refining the argument, we prove that for allβ>0 there existsρ(d,β)<d andN(d,β), such that for anyn>N(d,β), anyx ∈ ℤ d , and anyA ⊂ {1,…,n} d •{y∈ℤ whereν A,x (y) denotes the probability thaty is the first entrance point of the simple random walk starting atx intoA. Furthermore,ρ must converge tod asβ → ∞. Supported by Swiss NF grant 20-55648.98.  相似文献   

16.
Previously, we dubbed the conjecture that the alternating group An has no semiproportional irreducible characters for any natural n [1]. This conjecture was then shown to be equivalent to the following [3]. Let α and β be partitions of a number n such that their corresponding characters χα and χβ in the group Sn are semiproportional on An. Then one of the partitions α or β is self-associated. Here, we describe all pairs (α, β) of partitions satisfying the hypothesis and the conclusion of the latter conjecture. Supported by RFBR (grant No. 07-01-00148) and by RFBR-NSFC (grant No. 05-01-39000). __________ Translated from Algebra i Logika, Vol. 47, No. 2, pp. 135–156, March–April, 2008.  相似文献   

17.
The pseudorelativistic Hamiltonian is considered under wide conditions on potentials A(x), W(x). It is assumed that a real point λ is regular for G1/2. Let G1/2(α)=G1/2−αV, where α>0, V(x)≥0, and V ∈L d(ℝd). Denote by N(λ, α) the number of eigenvalues of G1/2(t) that cross the point λ as t increases from 0 to α. A Weyl-type asymptotics is obtained for N(λ, α) as α→∞. Bibliography: 5 titles. To O. A. Ladyzhenskaya Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 249, 1997. pp. 102–117. Translated by A. B. Pushnitskii.  相似文献   

18.
The two-parameter dyadic martingale Hardy spacesH p are introduced and it is proved that the maximal operator of the (C, α, β) means of a two-dimensional Walsh-Fourier series is bounded from Hp to Lp (1/(α+1), 1/(β+1)<p<∞) and is of weak type (H 1 # , L1), where the Hardy space H 1 # is defined by the hybrid maximal function. As a consequence, we obtain that the (C, α, β) means of a function f∈H 1 # converge a.e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on Hp whenever 1/(α+1), 1/(β+1)<p<∞. Thus in case f∈Hp, the (C, α, β) means converge to f in Hp norm. The same results are proved for the conjugate (C, α, β) means, too.  相似文献   

19.
In this paper, we study (α,β)-metrics of scalar flag curvature on a manifold M of dimension n (n 〉 3). Suppose that an (α,β)-metric F is not a Finsler metric of Randers type, that is, F ≠k1 V√α^2 + k2β^2 + k3β, where k1 〉 0, k2 and k3 are scalar functions on M. We prove that F is of scalar flag curvature and of vanishing S-curvature if metric. In this case, F is a locally Minkowski and only if the flag curvature K = 0 and F is a Berwald metric.  相似文献   

20.
Given an extremal process X: [0,∞)→[0,∞)d with lower curve C and associated point process N={(tk, Xk):k≥0}, tk distinct and Xk independent, given a sequence ζ n =(τ n , ξ n ), n≥1, of time-space changes (max-automorphisms of [0,∞)d+1), we study the limit behavior of the sequence of extremal processes Yn(t)=ξ n -1 ○ X ○ τn(t)=Cn(t) V max {ξ n -1 ○ Xk: tk ≤ τn(t){ ⇒ Y under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn. The limit class consists of self-similar (with respect to a group ηα=(σα, Lα), α>0, of time-space changes) extremal processes. By self-similarity here we mean the property Lα ○ Y(t) = d Y ○ αα(t) for all α>0. The univariate marginals of Y are max-self-decomposable. If additionally the initial extremal process X is assumed to have homogeneous max-increments, then the limit process is max-stable with homogeneous max-increments. Supported by the Bulgarian Ministry of Education and Sciences (grant No. MM 234/1996). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I.  相似文献   

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