共查询到20条相似文献,搜索用时 31 毫秒
1.
Andreas Greven Achim Klenke Anton Wakolbinger 《Probability Theory and Related Fields》2001,120(1):85-117
We study the longtime behaviour of interacting systems in a randomly fluctuating (space–time) medium and focus on models
from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and
interacting Fisher–Wright diffusions. Quite a bit is known on spatial branching processes where the local branching rate is
proportional to a random environment (catalytic medium).
Here we introduce a model of interacting Fisher–Wright diffusions where the local resampling rate (or genetic drift) is proportional
to a catalytic medium. For a particular choice of the medium, we investigate the longtime behaviour in the case of nearest
neighbour migration on the d-dimensional lattice.
While in classical homogeneous systems the longtime behaviour exhibits a dichotomy along the transience/recurrence properties
of the migration, now a more complicated behaviour arises. It turns out that resampling models in catalytic media show phenomena
that are new even compared with branching in catalytic medium.
Received: 15 November 1999 / Revised version: 16 June 2000 / Published online: 6 April 2001 相似文献
2.
Antoine Lejay 《Probability Theory and Related Fields》2001,120(2):255-276
The probabilistic machinery (Central Limit Theorem, Feynman-Kac formula and Girsanov Theorem) is used to study the homogenization
property for PDE with second-order partial differential operator in divergence-form whose coefficients are stationary, ergodic
random fields. Furthermore, we use the theory of Dirichlet forms, so that the only conditions required on the coefficients
are non-degeneracy and boundedness.
Received: 27 August 1999 / Revised version: 27 October 2000 / Published online: 26 April 2001 相似文献
3.
Peter Mörters 《Probability Theory and Related Fields》2000,118(1):49-64
The Kallianpur–Robbins law describes the long term asymptotic behaviour of integrable additive functionals of Brownian motion
in the plane. In this paper we prove an almost sure version of this result. It turns out that, differently from many known
results, this requires an iterated logarithmic average. A similar result is obtained for the small scales asymptotic by means
of an ergodic theorem of Chacon–Ornstein type, which allows an exceptional set of scales.
Received: 8 May 1998 / Revised version: 1 December 1999 / Published online: 8 August 2000 相似文献
4.
Michel Talagrand 《Probability Theory and Related Fields》2000,117(3):303-360
We prove that, just below the critical temperature, the mean field p-spins interaction model, for p suitably large, spontaneously decomposes into different states. The asymptotic overlaps between any two different states
are zero. Under a mild (unproven) hypothesis on the weight distribution of these states, we prove that they are pure states.
This situation is called in physics “one level of symmetry breaking”.
Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000 相似文献
5.
We consider the flow of a stochastic differential equation on d-dimensional Euclidean space. We show that if the Lie algebra generated by its diffusion vector fields is finite dimensional
and solvable, then the flow is conjugate to the flow of a non-autonomous random differential equation, i.e. one can be transformed
into the other via a random diffeomorphism of d-dimensional Euclidean space. Viewing a stochastic differential equation in this form which appears closer to the setting
of ergodic theory, can be an advantage when dealing with asymptotic properties of the system. To illustrate this, we give
sufficient criteria for the existence of global random attractors in terms of the random differential equation, which are
applied in the case of the Duffing-van der Pol oscillator with two independent sources of noise.
Received: 25 May 1999 / Revised version: 19 October 2000 / Published online: 26 April 2001 相似文献
6.
Zakhar Kabluchko 《Extremes》2009,12(4):401-424
To each max-stable process with α-Fréchet margins, α ∈ (0,2), a symmetric α-stable process can be associated in a natural way. Using this correspondence, we deduce known and new results on spectral
representations of max-stable processes from their α-stable counterparts. We investigate the connection between the ergodic properties of a stationary max-stable process and
the recurrence properties of the non-singular flow generating its spectral representation. In particular, we show that a stationary
max-stable process is ergodic iff the flow generating its spectral representation has vanishing positive recurrent component.
We prove that a stationary max-stable process is ergodic (mixing) iff the associated SαS process is ergodic (mixing). We construct non-singular flows generating the max-stable processes of Brown and Resnick. 相似文献
7.
Michel Talagrand 《Probability Theory and Related Fields》2000,117(4):449-466
In the previous paper in this volume we have studied the p-spin interaction model just below the critical temperature, and we have rigorously proved several aspects of the physicists
prediction that this model exhibits “one level of symmetry breaking”. In the present paper we show how to construct systems
that exhibit an arbitrarily large, but finite number of “levels of symmetry-breaking”. As the temperature decreases, such
systems exhibit many phase transitions, as the structure of the overlaps gains complexity. This phenomenon does not seem to
have been described previously, even in the physics literature.
Received: 15 January 1998 / Revised version: 10 November 1999 / Published online: 21 June 2000 相似文献
8.
Wojciech Młtkowski 《Probability Theory and Related Fields》1999,115(4):579-596
We study noncommutative probability spaces endowed with infinite sequences of states. Following ideas of Cabanal-Duvillard
we extend the notion of conditional freeness. Free product of such spaces is justified by constructing an appropriate ⋆-representation.
Finally, we provide limit theorems and describe the sequences of orthogonal polynomials related to the limit measures.
Received: 4 November 1998 / Revised version: 22 April 1999 相似文献
9.
If r is a reducibility between sets of numbers, a natural question to ask about the structure ?
r
of the r-degrees containing computably enumerable sets is whether every element not equal to the greatest one is branching (i.e.,
the meet of two elements strictly above it). For the commonly studied reducibilities, the answer to this question is known
except for the case of truth-table (tt) reducibility. In this paper, we answer the question in the tt case by showing that
every tt-incomplete computably enumerable truth-table degree a is branching in ?
tt
. The fact that every Turing-incomplete computably enumerable truth-table degree is branching has been known for some time.
This fact can be shown using a technique of Ambos-Spies and, as noticed by Nies, also follows from a relativization of a result
of Degtev. We give a proof here using the Ambos-Spies technique because it has not yet appeared in the literature. The proof
uses an infinite injury argument. Our main result is the proof when a is Turing-complete but tt-incomplete. Here we are able to exploit the Turing-completeness of a in a novel way to give a finite injury proof.
Received: 22 January 1999 / Revised version: 12 July 1999 / Published online: 21 December 2000 相似文献
10.
Sompolinski and Zippelius (1981) propose the study of dynamical systems whose invariant measures are the Gibbs measures for
(hard to analyze) statistical physics models of interest. In the course of doing so, physicists often report of an “aging”
phenomenon. For example, aging is expected to happen for the Sherrington-Kirkpatrick model, a disordered mean-field model
with a very complex phase transition in equilibrium at low temperature. We shall study the Langevin dynamics for a simplified
spherical version of this model. The induced rotational symmetry of the spherical model reduces the dynamics in question to
an N-dimensional coupled system of Ornstein-Uhlenbeck processes whose random drift parameters are the eigenvalues of certain random
matrices. We obtain the limiting dynamics for N approaching infinity and by analyzing its long time behavior, explain what is aging (mathematically speaking), what causes
this phenomenon, and what is its relationship with the phase transition of the corresponding equilibrium invariant measures.
Received: 8 July 1999 / Revised version: 2 June 2000 / Published online: 6 April 2001 相似文献
11.
The central limit theorem for Markov chains with normal transition operators, started at a point 总被引:2,自引:0,他引:2
The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov
chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point,
almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains
whose transition operator is normal.
Received: 28 March 2000 / Revised version: 25 July 2000 /?Published online: 15 February 2001 相似文献
12.
Albert Visser 《Archive for Mathematical Logic》2001,40(4):277-295
A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of
formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class
of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.
In Appendix A we prove that for theories with decidable identity we can take as the embeddings between domains in Kripke models
of the theory, the identical embeddings. This is a well known fact, but we know of no correct proof in the literature. In
Appendix B we answer, negatively, a question posed by Sam Buss: whether there is a classical theory T, such that ℋT is HA. Here ℋT is the theory of all Kripke models ℳ such that the structures assigned to the nodes of ℳ all satisfy T in the sense of classical model theory.
Received: 4 February 1999 / Published online: 25 January 2001 相似文献
13.
We prove that for each minimal rotation on a compact metric group and each topological cocycle , either φ is a topological coboundary, or is topologically ergodic, or the partition into orbits is the decomposition of into minimal components. As an application, we generalize a result by Glasner and show that if is a minimal topologically weakly mixing flow, then whenever φ is universally ergodic the minimal map
is not PI but is disjoint from all minimal topologically weakly mixing systems.
(Received 14 June 1999; in final form 28 September 2001) 相似文献
14.
The main result in this paper states that if a one-parameter Gaussian process has C
2k
paths and satisfies a non-degeneracy condition, then the distribution of its maximum on a compact interval is of class C
k
. The methods leading to this theorem permit also to give bounds on the successive derivatives of the distribution of the
maximum and to study their asymptotic behaviour as the level tends to infinity.
Received: 14 May 1999 / Revised version: 18 October 1999 / Published online: 14 December 2000 相似文献
15.
Leonid Polterovich 《Journal of the European Mathematical Society》1999,1(1):87-107
Let G be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold Y. A loop h:S1→G is called strictly ergodic if for some irrational number α the associated skew product map T:S1×Y→S1×Y defined by T(t,y)=(t+α,h(t)y) is strictly ergodic. In the present paper we address the following question. Which elements
of the fundamental group of G can be represented by strictly ergodic loops? We prove existence of contractible strictly ergodic
loops for a wide class of symplectic manifolds (for instance for simply connected ones). Further, we find a restriction on
the homotopy classes of smooth strictly ergodic loops in the framework of Hofer’s bi-invariant geometry on G. Namely, we prove
that their asymptotic Hofer’s norm must vanish. This result provides a link between ergodic theory and symplectic topology.
Received July 7, 1998 / final version received September 14, 1998 相似文献
16.
In this paper we show that shifts of finite type satisfying a strong topological mixing property are universal models for ergodic measure preserving
dynamical systems.
(Received 21 July 1999; in revised form 4 November 2000) 相似文献
17.
Answering a question raised by Glasner and Rudolph (1984) we construct uncountably many strictly ergodic topological systems
which are metrically isomorphic to a given ergodic system (X, ℬ,μ, T) but not almost topologically conjugate to it.
This paper is part of the second author’s Ph.D. thesis, written under the supervision of Professor A. Bellow of the Department
of Mathematics, Northwestern University. The author is grateful for her encouragement and advice.
We acknowledge B. Weiss for helpful comments. 相似文献
18.
Dinah Rosenberg Eilon Solan Nicolas Vieille 《Probability Theory and Related Fields》2001,119(3):433-451
We study stopping games in the setup of Neveu. We prove the existence of a uniform value (in a sense defined below), by allowing
the players to use randomized strategies. In constrast with previous work, we make no comparison assumption on the payoff
processes. Moreover, we prove that the value is the limit of discounted values, and we construct ε-optimal strategies.
Received: 10 May 1999 / Revised version: 18 May 2000 / Published online: 15 February 2001 相似文献
19.
Paul Seignourel 《Probability Theory and Related Fields》2000,118(3):293-322
We present discrete schemes for processes in random media. We prove two results. The first one is the convergence of Sinai's
random walks in random environments to the Brox model. The second one is the convergence of random walks in media with random
“gates” to a continuous process in a Poisson potential. The proofs are based on the following idea: we consider the discrete
media as random potentials for continuous models.
Received: 6 May 1999 / Revised version: 18 October 1999 / Published online: 20 October 2000 相似文献
20.
We consider an infinite tandem queueing network consisting of ·/GI/1/∞ stations with i.i.d. service times. We investigate the asymptotic behavior of t(n, k), the inter-arrival times between customers n and n + 1 at station k, and that of w(n, k), the waiting time of customer n at station k. We establish a duality property by which w(n, k) and the “idle times”y(n, k) play symmetrical roles. This duality structure, interesting by itself, is also instrumental in proving some of the ergodic
results. We consider two versions of the model: the quadrant and the half-plane. In the quadrant version, the sequences of
boundary conditions {w(0,k), k∈ℕ} and {t(n, 0), n∈ℕ}, are given. In the half-plane version, the sequence {t(n, 0), n∈ℕ} is given. Under appropriate assumptions on the boundary conditions and on the services, we obtain ergodic results for
both versions of the model. For the quadrant version, we prove the existence of temporally ergodic evolutions and of spatially
ergodic ones. Furthermore, the process {t(n, k), n∈ℕ} converges weakly with k to a limiting distribution, which is invariant for the queueing operator. In the more difficult half plane problem, the aim
is to obtain evolutions which are both temporally and spatially ergodic. We prove that 1/n∑
k=1
n
w(0, k) converges almost surely and in L
1 to a finite constant. This constitutes a first step in trying to prove that {t(n,k), n∈ℤ} converges weakly with k to an invariant limiting distribution.
Received: 23 March 1999 / Revised version: 5 January 2000 / Published online: 12 October 2000 相似文献