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1.
Péter Major 《Probability Theory and Related Fields》2006,134(3):489-537
Let a sequence of iid. random variables ξ
1, . . . ,ξ
n
be given on a space
with distribution μ together with a nice class
of functions f(x
1, . . . ,x
k
) of k variables on the product space
For all f ∈
we consider the random integral J
n,k
(f) of the function f with respect to the k-fold product of the normalized signed measure
where μ
n
denotes the empirical measure defined by the random variables ξ
1, . . . ,ξ
n
and investigate the probabilities
for all x>0. We show that for nice classes of functions, for instance if
is a Vapnik–Červonenkis class, an almost as good bound can be given for these probabilities as in the case when only the
random integral of one function is considered. A similar result holds for degenerate U-statistics, too.
Supported by the OTKA foundation Nr. 037886 相似文献
2.
Yu Zhang 《Probability Theory and Related Fields》2006,136(2):298-320
We consider the first passage percolation model on Z
d
for d ≥ 2. In this model, we assign independently to each edge the value zero with probability p and the value one with probability 1−p. We denote by T(0, ν) the passage time from the origin to ν for ν ∈ R
d
and
It is well known that if p < p
c
, there exists a compact shape B
d
⊂ R
d
such that for all
> 0,
t
B
d
(1 −
) ⊂ B(t) ⊂ tB
d
(1 +
) and G(t)(1 −
) ⊂ B(t) ⊂ G(t)(1 +
) eventually w.p.1. We denote the fluctuations of B(t) from tB
d
and G(t) by
In this paper, we show that for all d ≥ 2 with a high probability, the fluctuations F(B(t), G(t)) and F(B(t), tB
d
) diverge with a rate of at least C log t for some constant C. The proof of this argument depends on the linearity between the number of pivotal edges of all minimizing paths and the
paths themselves. This linearity is also independently interesting.
Research supported by NSF grant DMS-0405150 相似文献
3.
For a random closed set obtained by exponential transformation of the closed range of a subordinator, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of . We focus on the number of parts Kn of the composition when is derived from a gamma subordinator. We prove logarithmic asymptotics of the moments and central limit theorems for Kn and other functionals of the composition such as the number of singletons, doubletons, etc. This study complements our previous
work on asymptotics of these functionals when the tail of the Lévy measure is regularly varying at 0+.
Research supported in part by N.S.F. Grant DMS-0071448 相似文献
4.
Attila Wiebe 《manuscripta mathematica》2006,120(1):27-38
Let R be a positive normal affine semigroup ring of dimension d and let be the maximal homogeneous ideal of R. We show that the integral closure of is equal to for all n ∈ℕ with n ≥ d − 2. From this we derive that the Rees algebra R[t] is normal in case that d ≤ 3. If emb dim(R) = d + 1, we can give a necessary and sufficient condition for R[t] to be normal. 相似文献
5.
We describe the possible restrictions of the cotangent bundle to an elliptic curve . We apply this in positive characteristic to the computation of the Hilbert-Kunz function of a homogeneous R+-primary ideal in the graded section ring . 相似文献
6.
T. Bodineau 《Probability Theory and Related Fields》2006,135(2):153-168
We prove that all the translation invariant Gibbs states of the Ising model are a linear combination of the pure phases for any . This implies that the average magnetization is continuous for . Furthermore, combined with previous results on the slab percolation threshold [B2] this shows the validity of Pisztora's
coarse graining [Pi] up to the critical temperature.
We would like to thank C. Pfister and Y. Velenik for very useful comments. 相似文献
7.
S. Fourati 《Probability Theory and Related Fields》2006,135(2):201-215
We proove a new duality relation between stable Lévy processes with index and those with index . This duality appears to be the trajectorial version of the duality of Zolotarev which concerns one dimensional stable laws.
We give an application of this result to the behaviour of the paths at small and large times of the process ``conditioned
to stay positive'.
Mots-clefs: Lévy process Stable process Fluctuation identities Ladder process 相似文献
8.
Veronica Umanità 《Probability Theory and Related Fields》2006,134(4):603-623
We show that a QMS on a σ-finite von Neumann algebra can be decomposed as the sum of several ``sub'-semigroups corresponding to transient and recurrent projections. We discuss
two applications to physical models. 相似文献
9.
We prove that a complete embedded maximal surface in = (3, dx12 + dx22-dx32) with a finite number of singularities is an entire maximal graph with conelike singularities over any spacelike plane, and so, it is asymptotic to a spacelike plane or a half catenoid. We show that the moduli space of entire maximal graphs over {x3=0} in with n+12 singular points and vertical limit normal vector at infinity is a 3n+4-dimensional differentiable manifold. The convergence in means the one of conformal structures and Weierstrass data, and it is equivalent to the uniform convergence of graphs on compact subsets of {x3=0}. Moreover, the position of the singular points in 3 and the logarithmic growth at infinity can be used as global analytical coordinates with the same underlying topology. We also introduce the moduli space of marked graphs with n+1 singular points (a mark in a graph is an ordering of its singularities), which is a (n+1)-sheeted covering of . We prove that identifying marked graphs differing by translations, rotations about a vertical axis, homotheties or symmetries about a horizontal plane, the corresponding quotient space is an analytic manifold of dimension 3n–1. This manifold can be identified with a spinorial bundle associated to the moduli space of Weierstrass data of graphs in .Mathematics Subject Classification (2000): 53C50, 58D10, 53C42First and second authors research partially supported by MEC-FEDER grant number MTM2004-00160Second and third authors research partially supported by Consejería de Educación y Ciencia de la Junta de Andalucía and the European Union. 相似文献
10.
Jérémy Blanc 《manuscripta mathematica》2006,119(2):225-241
We describe the conjugacy classes of affine automorphisms in the group Aut(n,) (respectively Bir()) of automorphisms (respectively of birational maps) of . From this we deduce also the classification of conjugacy classes of automorphisms of ℙn in the Cremona group Bir(). 相似文献
11.
Christoph Scheven 《Mathematische Zeitschrift》2006,253(1):135-157
Let and be smooth Riemannian manifolds, of the dimension n≥2 with nonempty boundary, and compact without boundary. We consider stationary harmonic maps u ∈ H1(, ) with a free boundary condition of the type u(∂) ⊂ Γ, given a submanifold Γ⊂. We prove partial boundary regularity, namely (sing(u))=0, a result that was until now only known in the interior of the domain (see [B]). The key of the proof is a new lemma
that allows an extension of u by a reflection construction. Once the partial regularity theorem is known, it is possible to reduce the dimension of the
singular set further under additional assumptions on the target manifold and the submanifold Γ. 相似文献
12.
Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times n along which we will be able to estimate the conditional probability P(=x|X0,...,) from data segment (X0,...,) in a pointwise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet time series which includes among others all stationary and ergodic finitarily Markovian processes. If the stationary and ergodic process turns out to be finitarily Markovian (among others, all stationary and ergodic Markov chains are included in this class) then almost surely. If the stationary and ergodic process turns out to possess finite entropy rate then n is upperbounded by a polynomial, eventually almost surely.Mathematics Subject Classification (2000): 62G05, 60G25, 60G10 相似文献
13.
Sven Winklmann 《manuscripta mathematica》2005,118(4):485-499
We consider immersed hypersurfaces :Mn→ℝn+1 with prescribed anisotropic mean curvature . Such hypersurfaces can be characterized as critical points of parametric functionals of the type with an elliptic Lagrangian F depending on normal directions and a smooth vectorfield Q satisfying . We establish curvature estimates for stable hypersurfaces of dimension n≤5, provided F is C3-close to the area integrand. 相似文献
14.
Yongpei Guan Shabbir Ahmed George L. Nemhauser Andrew J. Miller 《Mathematical Programming》2006,105(1):55-84
This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under
uncertainty. We show that the classical (ℓ,S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend
the (ℓ,S) inequalities to a general class of valid inequalities, called the inequalities, and we establish necessary and sufficient conditions which guarantee that the inequalities are facet-defining. A separation heuristic for inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness
of the inequalities as cuts.
This research has been supported in part by the National Science Foundation under Award number DMII-0121495. 相似文献
15.
In this paper, we provide a suitable theory for the energy
where μ is a Radon measure and Γ is the fundamental solution of a sub-Laplacian on a stratified group As a significant application, we prove the quasi-continuity of superharmonic functions related to . The proofs are elementary and mostly rely on the use of appropriate mean-value formulas and mean-integral operators relevant
to the Potential Theory for . 相似文献
16.
In the bootstrap percolation on the n-dimensional hypercube, in the initial position each of the 2n sites is occupied with probability p and empty with probability 1−p, independently of the state of the other sites. Every occupied site remains occupied for ever, while an empty site becomes
occupied if at least two of its neighbours are occupied. If at the end of the process every site is occupied, we say that
the (initial) position spans the hypercube. We shall show that there are constants c1,c2>0 such that for the probability of spanning tends to 1 as n→∞, while for the probability tends to 0. Furthermore, we shall show that for each n the transition has a sharp threshold function.
J. Balogh: work was done while at The University of Memphis, USA
Research supported in part by NSF grant DMS0302804
Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900 相似文献
17.
Hideyo Sasaki 《manuscripta mathematica》2006,119(1):97-106
Let be a real quadratic field with m a square-free positive rational integer, and be the ring of integers in F. An -lattice L on a totally positive definite quadratic space V over F is called r-universal if L represents all totally positive definite -lattices l with rank r over . We prove that there exists no 2-universal -lattice over F with rank less than 6, and there exists a 2-universal -lattice over F with rank 6 if and only if m=2, 5. Moreover there exists only one 2-universal -lattice with rank 6, up to isometry, over . 相似文献
18.
Valentin Savin 《manuscripta mathematica》2006,119(3):287-303
Let = [X/G] be the quotient stack of a scheme X by an affine group scheme G over a field k. Assume that there is a line bundle on whose underlying line bundle on X is very ample. Let VB() be the category of vector bundles on .We show that is canonically isomorphic to the stack of fiber functors on VB(). This is an analogue of the Tannaka duality for affine groups.
Partially supported by CNCSIS contract no. 33079/2004 相似文献
19.
Michel Talagrand 《Probability Theory and Related Fields》2006,135(4):471-486
Consider the random subset X of ℕ obtained by selecting independently each integer with a probability δ. Consider a finite class of finite sets. We describe a combinatorial quantity that is of the same order as We then give a related result allowing to compute the supremum of the empirical process on a class of sets.
Work partially supported by an NSF grant. 相似文献
20.
The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal
logic [26], intuitionistic logic without contraction [1], HBCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from
that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses.
It results that this notion of fragment is axiomatized by the rules of the sequent calculus for the connectives involved. We also prove that these deductive systems are non-protoalgebraic, while the Gentzen systems
are algebraizable with equivalent algebraic semantics the varieties of pseudocomplemented (commutative integral bounded) semilatticed
and latticed monoids, respectively. All the logical systems considered are decidable. 相似文献