共查询到20条相似文献,搜索用时 31 毫秒
1.
László Erdo˝s 《Probability Theory and Related Fields》2001,121(2):219-236
We establish the exact low-energy asymptotics of the integrated density of states (Lifschitz tail) in a homogeneous magnetic
field and Poissonian impurities with a repulsive single-site potential of Gaussian decay. It has been known that the Gaussian
potential tail discriminates between the so-called “classical” and “quantum” regimes, and precise asymptotics are known in
these cases. For the borderline case, the coexistence of the classical and quantum regimes was conjectured. Here we settle
this last remaining open case to complete the full picture of the magnetic Lifschitz tails.
Received: 28 March 2000 / Revised version: 22 December 2000 / Published online: 24 July 2001 相似文献
2.
We derive rough and exact asymptotic expressions for the stationary distribution π of a Markov chain arising in a queueing/production context. The approach we develop can also handle “cascades,” which are
situations where the fluid limit of the large deviation path from the origin to the increasingly rare event is nonlinear.
Our approach considers a process that starts at the rare event. In our production example, we can have two sequences of states
that asymptotically lie on the same line, yet π has different asymptotics on the two sequences. 相似文献
3.
The asymmetric leader election algorithm has obtained quite a bit of attention lately. In this paper we want to analyze the
following asymptotic properties of the number of rounds: Limiting distribution function, all moments in a simple automatic
way, asymptotics for p → 0, p → 1 (where p denotes the “killing” probability). This also leads to a few interesting new identities. We use two paradigms: First, in
some urn model, we have asymptotic independence of urns behaviour as far as random variables related to urns with a fixed
number of balls are concerned. Next, we use a technique easily leading to the asymptotics of the moments of extremevalue related
distribution functions.
相似文献
4.
S. M. Anan'evskii 《Journal of Mathematical Sciences》1999,93(3):259-264
A modified “parking” problem is considered. Segments of different length fill a large interval (in our case, there are two
kinds of segments). The asymptotics of the mean number of segmentsplaced are obtained. Bibliography: 2 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 16–23. 相似文献
5.
In this article, we consider a stationary α-mixing random field in IR
d. Under a large-sample scheme that is a mixture of the so-called “infill” and “increasing domain” asymptotics, we establish
a functional central limit theorem for the empirical processes of this random field. Further, we apply a blockwise bootstrap
to the samples. Under the condition that the side length of the block
for some 0 < β < 1, where λ
n
is the growth rate in the increasing domain asymptotics, we show that the bootstrapped empirical process converges weakly
to the same limiting Gaussian process almost surely. Extension to multivariate random fields and application to differentiable
statistical functionals are also given. A spatial version of the Bernstein’s inequality is developed, which may be of some
independent interest.
In final form 13 December 2004 相似文献
6.
Serguei Foss Takis Konstantopoulos Stan Zachary 《Journal of Theoretical Probability》2007,20(3):581-612
We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural
conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the
process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make
full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs
are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks. 相似文献
7.
Avinoam Mann 《Israel Journal of Mathematics》1973,14(3):294-303
We investigate minimal irregularp-groups, and derive several criteria for regularity as a consequence. For example, ap-group is regular if all its subgroups have “few” generators. It is also shown that for varieties, regularity is equivalent
to “good” power structure. We slose with some examples. 相似文献
8.
The typical approach in change-point theory is to perform the statistical analysis based on a sample of fixed size. Alternatively, and this is our approach, one observes some random phenomenon sequentially and takes action as soon as one observes some statistically significant deviation from the “normal” behaviour. In this paper we focus on epidemic changes, that is, a first change (the outbreak) when there is a change in the distribution, and a second change, when the process regains its ordinary structure. Based on the counting process related to the original process observed at equidistant time points, we propose some stopping rules for this to happen and consider their asymptotics under the null hypothesis as well as under alternatives. The main basis for the proofs are strong invariance principles for renewal processes, extreme value asymptotics for Gaussian processes, and the law of the iterated logarithm. 相似文献
9.
Amir Dembo Nina Gantert Yuval Peres Ofer Zeitouni 《Probability Theory and Related Fields》2002,122(2):241-288
In the study of large deviations for random walks in random environment, a key distinction has emerged between quenched asymptotics, conditional on the environment, and annealed asymptotics, obtained from averaging over environments. In this paper we consider a simple random walk {X
n
} on a Galton–Watson tree T, i.e., on the family tree arising from a supercritical branching process. Denote by |X
n
| the distance between the node X
n
and the root of T. Our main result is the almost sure equality of the large deviation rate function for |X
n
|/n under the “quenched measure” (conditional upon T), and the rate function for the same ratio under the “annealed measure” (averaging on T according to the Galton–Watson distribution). This equality hinges on a concentration of measure phenomenon for the momentum of the walk. (The momentum at level n, for a specific tree T, is the average, over random walk paths, of the forward drift at the hitting point of that level). This concentration, or
certainty, is a consequence of the uncertainty in the location of the hitting point. We also obtain similar results when {X
n
} is a λ-biased walk on a Galton–Watson tree, even though in that case there is no known formula for the asymptotic speed.
Our arguments rely at several points on a “ubiquity” lemma for Galton–Watson trees, due to Grimmett and Kesten (1984).
Received: 15 November 2000 / Revised version: 27 February 2001 / Published online: 19 December 2001 相似文献
10.
Rayleigh waves in an almost layered viscoelastic medium are studied by using the “surface” ray method based on real rays.
Viscoelasticity is described in terms of the Maxwell-Boltzmann-Volterra model and, for high frequencies, is treated as perturbed
perfect elasticity. In addition to the leading term of the ray asymptotics, which corresponds to the balance of energy along
rays, the correction term describing anomalous displacements of the Love type is discussed. Bibliography: 10 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 7–13. 相似文献
11.
We study the R-controllability (the controllability within the attainability set) and the R-observability of time-varying linear differential-algebraic equations (DAE). We analyze DAE under assumptions guaranteeing
the existence of a structural form (which is called “equivalent”) with separated “differential” and “algebraic” subsystems.
We prove that the existence of this form guarantees the solvability of the corresponding conjugate system, and construct the
corresponding “equivalent form” for the conjugate DAE. We obtain conditions for the R-controllability and R-observability, in particular, in terms of controllability and observability matrices. We prove theorems that establish certain
connections between these properties. 相似文献
12.
M. O. Korpusov A. G. Sveshnikov 《Computational Mathematics and Mathematical Physics》2011,51(3):377-403
A model equation is considered that describes the relaxation of an initial perturbation in a crystalline semiconductor in
the case when its electrical conductivity depends nonlocally on the field. For certain initial parameters, the effect of finite-time
“cooling” is proved to occur. For other parameters, the first term of the long-time asymptotics is found and the remainder
of the asymptotic expansion is estimated. 相似文献
13.
We answer Hubbard's question on determining the Thurston equivalence class of “twisted rabbits”, i.e. composita of the “rabbit” polynomial with nth powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of n. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions. 相似文献
14.
In this paper we study the asymptotics of the discrete spectrum in the gap (−1, 1) of the perturbed Dirac operatorD(α)=D
0−αV1 acting inL
2(R
3;C
4) with large coupling constant α. In particular some “non-standard” asymptotic formulae are obtained. 相似文献
15.
M. D. Surnachev 《Differential Equations》2009,45(8):1174-1188
We obtain an asymptotic representation of solutions of equations of the Emden-Fowler type with “supercritical” exponent and
prove the existence of solutions with a given asymptotics. The methods used include the construction of supersolutions for
deriving a priori estimates and the use of Kondrat’ev’s results for weighted spaces. The existence of solutions is proved
by the Leray-Schauder method. 相似文献
16.
17.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
18.
Summary As a criterion for the reduction to a complete class of decision rule in case where actions, samples and states are finite
in number, “regret-relief ratio” criterion and “incremental loss-gain ratio” criterion were introduced in 2-state of nature
case [2]. In this paper, “generalized regret-relief ratio” criterion ink-state of nature case is introduced as an extension of “regret-relief ratio” criterion and its usefulness is shown with an
example.
The Institute of Statistical Mathematics 相似文献
19.
Maury Bramson J. Theodore Cox David Griffeath 《Probability Theory and Related Fields》1986,73(4):613-625
Summary This paper is a sequel of a paper of Cox and Griffeath “diffusive clustering in the two dimensional voter model”. We continue
our study of the voter model and coalescing random walks on the two dimensional integer lattice. Some exact asymptotics concerning
the rate of clustering in the former process and the coalescence rate of the latter are derived. We use these results to prove
a limit law, announced in that earlier paper, concerning the size of the largest square centered at the origin which is of
solid color at a large time t.
Partially supported by the National Science Foundation under Grant DMS-831080
Partially supported by the National Science Foundation under Grant DMS-841317
Partially supported by the National Science Foundation under Grant DMS-830549 相似文献
20.
Laurent Stolovitch 《Publications Mathématiques de L'IHéS》2005,102(1):99-165
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system.
The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first
integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets
in a neighborhood of the origin. These are biholomorphic to the intersection of a polydisc with an analytic set of the form
“resonant monomials = constants”. Such a biholomorphism conjugates the restriction of X to one of its invariant varieties
to the restriction of a linear diagonal vector field to a toric variety. Moreover, we show that the set of “frequencies” defining
the invariant sets is of positive measure. 相似文献