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1.
We present a topological analogue of the classic Kadec Renorming Theorem, as follows. Let be two separable metric topologies on the same set X. We prove that every point in X has an -neighbourhood basis consisting of sets that are -closed if and only if there exists a function φ: X→ℝ that is -lower semi-continuous and such that is the weakest topology on X that contains and that makes φ continuous. An immediate corollary is that the class of almost n-dimensional spaces consists precisely of the graphs of lower semi-continuous functions with at most n-dimensional domains. 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.
We study spectral multipliers of right invariant sub-Laplacians with drift on a connected Lie group G. The operators we consider are self-adjoint with respect to a positive measure , whose density with respect to the left Haar measure λG is a nontrivial positive character of G. We show that if p≠2 and G is amenable, then every spectral multiplier of extends to a bounded holomorphic function on a parabolic region in the complex plane, which depends on p and on the drift. When G is of polynomial growth we show that this necessary condition is nearly sufficient, by proving that bounded holomorphic functions
on the appropriate parabolic region which satisfy mild regularity conditions on its boundary are spectral multipliers of .
Work partially supported by the EC HARP Network “Harmonic Analysis and Related Problems”, the Progetto Cofinanziato MURST
“Analisi Armonica” and the Gruppo Nazionale INdAM per l'Analisi Matematica, la Probabilità e le loro Applicazioni. Part of
this work was done while the second and the third author were visiting the “Centro De Giorgi” at the Scuola Normale Superiore
di Pisa, during a special trimester in Harmonic Analysis. They would like to express their gratitude to the Centro for the
hospitality. 相似文献
4.
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
5.
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
6.
We investigate the large N behavior of the time the simple random walk on the discrete cylinder
needs to disconnect the discrete cylinder. We show that when d≥2, this time is roughly of order N
2
d
and comparable to the cover time of the slice
, but substantially larger than the cover timer of the base by the projection of the walk. Further we show that by the time
disconnection occurs, a massive ``clogging' typically takes place in the truncated cylinders of height
. These mechanisms are in contrast with what happens when d=1. 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.
Jon Warren 《Probability Theory and Related Fields》2005,133(4):559-572
A stochastic flow of homeomorphisms of previously studied by Bass and Burdzy [2] and Hu and Warren [4] is shown to arise in the study of the local times of Brownian
motion. This leads to a new proof of the Ray-Knight theorems for the flow via the classical Ray-Knight theorems for Brownian
motion. 相似文献
9.
Dumitru Popa 《Positivity》2006,10(1):87-94
We introduce in a natural way the notion of measure with bounded variation with respect to a normed ideal of operators and
prove that for each maximal normed ideal of operators (, ), is true the following result: If U ∈ L(C(T,X), Y) with G the representing measure of U and G : Σ → ((X, Y),) has bounded variation, then U ∈ (C(T,X), Y). As an application of this result we prove that an injective tensor product of an integral operator with an operator belonging
to a maximal normed ideal of operators (,) belongs also to (, ). 相似文献
10.
Baohua Fu 《Mathematische Zeitschrift》2006,253(1):87-96
We prove that two projective symplectic resolutions of are connected by Mukai flops in codimension 2 for a finite sub-group G <Sp(2n). It is also shown that two projective symplectic resolutions of are deformation equivalent. 相似文献
11.
Antonio Montalbán 《Archive for Mathematical Logic》2006,45(2):215-231
We prove that the existential theory of the Turing degrees, in the language with Turing reduction, 0, and unary relations
for the classes in the generalized high/low hierarchy, is decidable.
We also show that every finite poset labeled with elements of (where is the partition of induced by the generalized high/low hierarchy) can be embedded in preserving the labels. Note that no condition is imposed on the labels. 相似文献
12.
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
13.
Erlend Fornæss Wold 《Mathematische Zeitschrift》2006,252(1):1-9
We show that any finitely connected domain can be properly embedded into . For some sequences can also be properly embedded into . 相似文献
14.
We prove that the mean value of the real parts of the nontrivial zeros of the Epstein zeta-function associated with a positive definite quadratic form in n variables is equal to . Furthermore, we show that Epstein zeta-functions in general have an asymmetric zero-distribution with respect to the critical
line Re . 相似文献
15.
Sara Maad 《manuscripta mathematica》2005,116(3):357-384
We study the semilinear equationwhere is the Heisenberg Laplacian and is the Heisenberg group. The function f C2(×, ) is supposed to satisfy some (subcritical) growth conditions and to be left invariant under the action of the subgroup of consisting of points with integer coordinates.. We show the existence of infinitely many solutions in the space S12(), which is the Heisenberg analogue of the Sobolev space W1,2(N).Mathematics Subject Classification (2000): 22E30, 22E27 相似文献
16.
Lutz Mattner 《Probability Theory and Related Fields》2004,130(2):151-166
This is a contribution to the theory of sums of independent random variables at an algebraico-analytical level: Let Prob denote the convolution semigroup of all probability measures on with all moments finite, topologized by polynomially weighted total variation. We prove that the cumulant sequence regarded as a function from Prob into the additive topological group ofall real sequences, is universal among continuous homomorphisms from Prob into Hausdorff topological groups, in the usual sense that every other such homomorphism factorizes uniquely through . An analogous result, referring to just the first cumulants,holds for the semigroup of all probability measures with existing rth moments. In particular, there is no nontrivial continuous homomorphism from the convolution semigroup of all probability measures, topologized by the total variation metric, into any Hausdorff topological group.Mathematics Subject Classification (2000): 60B15, 60E10, 60G50 相似文献
17.
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
18.
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
19.
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
20.
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