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1.
We describe the statistics of repetition times of a string of symbols in a stochastic process.
Denote by τ
A
the time elapsed until the process spells a finite string A and by S
A
the number of consecutive repetitions of A. We prove that, if the length of the string grows unboundedly, (1) the distribution of τ
A
, when the process starts with A, is well approximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S
A
is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we
obtain are point-wise and also allow us to get approximations for all the moments of τ
A
and S
A
. To obtain (1) we assume that the process is φ-mixing, while to obtain (2) we assume the convergence of certain conditional probabilities.
相似文献
2.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
3.
In this paper, the notions of (p, λ)-Koszul algebra and (p, λ)-Koszul module are introduced. Some criteria theorems for a positively graded algebra A to be (p, λ)-Koszul are given. The notion of weakly (p, λ)-Koszul module is defined as well and let WK
λ
p
(A) denote the category of weakly (p, λ)-Koszul modules. We show that M ∈ WK
λ
p
(A) if and only if it can be approximated by (p, λ)-Koszul submodules, which is equivalent to that G(M) is a (p, λ)-Koszul module, where G(M) denotes the associated graded module of M. As applications, the relationships of the minimal graded projective resolutions of M, G(M) and (p, λ)-Koszul submodules are established. In particular, for a module M ∈ WK
λ
p
(A) we prove that ⊕
i≥0 Ext
A
i
(M,A
0) ∈ gr
0(E(A)), we also get as a consequence that the finitistic dimension conjecture is valid in WK
λ
p
(A) under certain conditions. 相似文献
4.
Tien-Cuong Dinh 《Journal of Geometric Analysis》2007,17(2):227-244
Let f be a holomorphic endomorphism of ℙ
k
having an attracting setA. We construct an attracting current and an equilibrium measure associated toA. The attracting current is weakly laminar and extremal in the cone of invariant currents. The equilibrium measure is mixing
and has maximal entropy onA. 相似文献
5.
We study iterated function systems of contractions which depend holomorphically on a complex parameter λ. We first restrict
our attention to systems which consist of similarities that satisfy the OSC. In this setting, we prove that the Hausdorff
dimension of the limit set J(λ) is a continuous, subharmonic function of λ. In the remainder of the paper, systems consisting of conformal contractions
are considered. We give conditions under which J(λ) and A(λ) =
describe a holomorphic motion, and construct an example that shows that this is not the case in general. We finally show
that A(λ) is best described as an analytic multifunction of λ, a notion that generalizes that of holomorphic motion.
This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Fonds Québécois
de Recherche sur la Nature et les Technologies (FQRNT).
This research was supported by the FQRNT. 相似文献
6.
It is proved that if a K?the space λ1(A) is distinguished and E is an arbitrary Fréchet space then every reflexive map T: λ1(A)→E (i.e., T maps bounded sets into relatively weakly compact ones) factorizes through a reflexive Fréchet space. An analogous result
is proved for Montel maps (i.e., which map bounded sets into relatively compact ones). The result is a consequence of the
fact proved also in this paper that, for a distinguished λ1(A) space, the spaces of reflexive maps R(λ1(A), C(K)) and of Montel maps M(λ1(A), C(K)) are the Mackey completions of the spaces of weakly compact and compact maps, respectively. Consequences for spaces of vector-valued
(weakly) continuous functions are also obtained.
Received: 24 November 1997 / Revised version: 14 May 1998 相似文献
7.
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ -1,1,2,3, and A, B ∈ B(H),A-λB ∈I(H) ⇔ Φ(A) -λΦ(B) ∈I(H, then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT
-1 for all A ∈ B(H), or Φ(A) = TA*T
-1 for all A ∈ B(H); if, in addition, A-iB ∈I(H)⇔ Φ(A)-iΦ(B) ∈I(H), here i is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
8.
Kenneth S. Alexander 《Probability Theory and Related Fields》1998,110(4):441-471
Summary. For lattice models on ℤ
d
, weak mixing is the property that the influence of the boundary condition on a finite decays exponentially with distance
from that region. For a wide class of models on ℤ2, including all finite range models, we show that weak mixing is a consequence of Gibbs uniqueness, exponential decay of an
appropriate form of connectivity, and a natural coupling property. In particular, on ℤ2, the Fortuin-Kasteleyn random cluster model is weak mixing whenever uniqueness holds and the connectivity decays exponentially,
and the q-state Potts model above the critical temperature is weak mixing whenever correlations decay exponentially, a hypothesis satisfied
if q is sufficiently large. Ratio weak mixing is the property that uniformly over events A and B occurring on subsets Λ and Γ, respectively, of the lattice, |P(A∩B)/P(A)P(B)−1| decreases exponentially in the distance between Λ and Γ. We show that under mild hypotheses, for example finite range,
weak mixing implies ratio weak mixing.
Received: 27 August 1996 / In revised form: 15 August 1997 相似文献
9.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,162(1):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
\frac12\frac{1}{2}
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism. 相似文献
10.
A. J. Hoffman 《Israel Journal of Mathematics》1974,17(1):69-75
To every symmetric matrixA with entries ±1, we associate a graph G(A), and ask (for two different definitions of distance) for the distance ofG(A) to the nearest complete bipartite graph (cbg). Letλ
1(A),λ
1 (A) be respectively the algebraically largest and least eigenvalues ofA. The Frobenius distance (see Section 4) to the nearest cbg is bounded above and below by functions ofn −λ
1 (A), wheren=ord A. The ordinary distance (see Section 1) to the nearest cbg is shown to be bounded above and below by functions ofλ
1 (A). A curious corollary is: there exists a functionf (independent ofn, and given by (1.1)), such that |λ
i
(A) | ≦f(λ
1(A), whereλ
i
(A) is any eigenvalue ofA other thanλ
i
(A).
This work was supported (in part) by the U.S. Army under contract #DAHC04-C-0023. 相似文献
11.
Let K be a convex body in the plane. Define λ(K,t) as the smallest number satisfying the following: if F\mathcal{F} is any family of translates of K such that every t members of F\mathcal{F} have a common transversal, then all the members of l(K,t)F\lambda(K,t)\mathcal{F} have a common transversal. We give bounds for λ(K,3) and λ(K,4) for a general convex figure K. In particular, we obtain that λ(K,3)≤1.79 when K is the Euclidean disc. 相似文献
12.
Palle E. T. Jorgensen Keri A. Kornelson Karen L. Shuman 《Journal of Fourier Analysis and Applications》2011,17(3):431-456
We study the harmonic analysis of Bernoulli measures μ
λ
, a one-parameter family of compactly supported Borel probability measures on the real line. The parameter λ is a fixed number in the open interval (0,1). The measures μ
λ
may be understood in any one of the following three equivalent ways: as infinite convolution measures of a two-point probability
distribution; as the distribution of a random power series; or as an iterated function system (IFS) equilibrium measure determined
by the two transformations λ(x±1). For a given λ, we consider the harmonic analysis in the sense of Fourier series in the Hilbert space L
2(μ
λ
). For L
2(μ
λ
) to have infinite families of orthogonal complex exponential functions e
2πis(⋅), it is known that λ must be a rational number of the form
\fracm2n\frac{m}{2n}, where m is odd. We show that
L2(m\frac12n)L^{2}(\mu_{\frac{1}{2n}}) has a variety of Fourier bases; i.e. orthonormal bases of exponential functions. For some other rational values of λ, we exhibit maximal Fourier families that are not orthonormal bases. 相似文献
13.
Mohamed Hmissi 《manuscripta mathematica》1992,75(1):293-302
Let ℙ=(P
t
)
t<0
be a semigroup of kernel and letm be an excessive reference measure for ℙ. In this work we prove that ℙ ism-basic if and only if everym.a.e. finite purely excessive function is represented by a unique exit law for ℙ. In this case we deduce some applications
about natural densities, energie functionnal and invariant functions for the time-space semigroup of ℙ.
相似文献
14.
Let
\mathfrakA\mathfrak{A} be a normed algebra with identity, Ω be a locally compact Hausdorf space and λ be a positive Radon measure on Ω with supp(λ) = Ω. In this paper, we establish a necessary and sufficient condition for L
1(Ω,
\mathfrakA\mathfrak{A}) to be an algebra with pointwise multiplication. Under this condition, we then characterize compact and weakly compact left
multipliers on L
1(Ω,
\mathfrakA\mathfrak{A}). 相似文献
15.
A local variational relation and applications 总被引:3,自引:0,他引:3
In [BGH] the authors show that for a given topological dynamical system (X,T) and an open coveru there is an invariant measure μ such that infh
μ(T,ℙ)≥h
top(T,U) where infimum is taken over all partitions finer thanu. We prove in this paper that if μ is an invariant measure andh
μ(T,ℙ) > 0 for each ℙ finer thanu, then infh
μ(T,ℙ > 0 andh
top(T,U) > 0. The results are applied to study the topological analogue of the Kolmogorov system in ergodic theory, namely uniform
positive entropy (u.p.e.) of ordern (n≥2) or u.p.e. of all orders. We show that for eachn≥2 the set of all topological entropyn-tuples is the union of the set of entropyn-tuples for an invariant measure over all invariant measures. Characterizations of positive entropy, u.p.e. of ordern and u.p.e. of all orders are obtained.
We could answer several open questions concerning the nature of u.p.e. and c.p.e.. Particularly, we show that u.p.e. of ordern does not imply u.p.e. of ordern+1 for eachn≥2. Applying the methods and results obtained in the paper, we show that u.p.e. (of order 2) system is weakly disjoint from
all transitive systems, and the product of u.p.e. of ordern (resp. of all orders) systems is again u.p.e. of ordern (resp. of all orders).
Project supported by one hundred talents plan and 973 plan. 相似文献
16.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,149(2):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism.
The third author is Corresponding author. 相似文献
17.
This article gives the representations of two types of real functionals on L
∞(Ω, Ƒ) or L
∞(Ω, Ƒ, ℙ) in terms of Choquet integrals. These functionals are comonotonically subadditive and comonotonically convex, respectively. 相似文献
18.
A mathematical program with a rational objective function may have irrational algebraic solutions even when the data are integral.
We suggest that for such problems the optimal solution will be represented as follows: If λ* denotes the optimal value there
will be given an intervalI and a polynomialP(λ) such thatI contains λ* and λ* is the unique root ofP(λ) inI. It is shown that with this representation the solutions to convex quadratic fractional programs and ratio games can be obtained
in polynomial time. 相似文献
19.
Let ƒ be a polynomial automorphism of ℂk of degree λ, whose rational extension to ℙk maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙk of bidegree (1,1), we show that the sequence λ−n(ƒn)*S converges in the sense of currents on ℙk to a linear combination of the Green current T+ of ƒ and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms
of generalized Lelong numbers with respect to an invariant dynamical current for ƒ−1. 相似文献
20.
Sergio Albeverio Zbignew Haba Francesco Russo 《Probability Theory and Related Fields》2001,121(3):319-366
A two-space dimensional heat equation perturbed by a white noise in a bounded volume is considered. The equation is perturbed
by a non-linearity of the type λ : f(AU) :, where :: means Wick (re)ordering with respect to the free solution;λ, A are small parameters, U denotes a solution, f is the Fourier transform of a complex measure with compact support.
Existence and uniqueness of the solution in a class of Colombeau-Oberguggenberger generalized functions is proven. An explicit
construction of the solution is given and it is shown that each term of the expansion in a power series in λ is associated
with an L
2-valued measure when A is a small enough.
Received: 20 July 1997 / Revised version: 1 February 2001 / Published online: 9 October 2001 相似文献