共查询到20条相似文献,搜索用时 0 毫秒
1.
Remco van der Hofstad Frank den Hollander Gordon Slade 《Probability Theory and Related Fields》1998,111(2):253-286
Summary. We introduce a new inductive approach to the lace expansion, and apply it to prove Gaussian behaviour for the weakly self-avoiding
walk on ℤ
d
where loops of length m are penalised by a factor e
−β/m p
(0<β≪1) when: (1) d>4, p≥0; (2) d≤4, . In particular, we derive results first obtained by Brydges and Spencer (and revisited by other authors) for the case d>4, p=0. In addition, we prove a local central limit theorem, with the exception of the case d>4, p=0.
Received: 29 October 1997 / In revised form: 15 January 1998 相似文献
2.
M.S. Bernabei 《Probability Theory and Related Fields》2001,119(3):410-432
The Central Limit Theorem for a model of discrete-time random walks on the lattice ℤν in a fluctuating random environment was proved for almost-all realizations of the space-time nvironment, for all ν > 1 in
[BMP1] and for all ν≥ 1 in [BBMP]. In [BMP1] it was proved that the random correction to the average of the random walk for
ν≥ 3 is finite. In the present paper we consider the cases ν = 1,2 and prove the Central Limit Theorem as T→∞ for the random correction to the first two cumulants. The rescaling factor for theaverage is for ν = 1 and (ln T), for ν=2; for the covariance it is , ν = 1,2.
Received: 25 November 1999 / Revised version: 7 June 2000 / Published online: 15 February 2001 相似文献
3.
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
4.
We prove that the process of the most visited site of Sinai's simple random walk in random environment is transient. The
rate of escape is characterized via an integral criterion. Our method also applies to a class of recurrent diffusion processes
with random potentials. It is interesting to note that the corresponding problem for the usual symmetric Bernoulli walk or
for Brownian motion remains open.
Received: 17 April 1998 相似文献
5.
Christiane Takacs 《Probability Theory and Related Fields》1998,111(1):123-139
Summary. We define directed rooted labeled and unlabeled trees and find measures on the space of directed rooted unlabeled trees which
are invariant with respect to transition probabilities corresponding to a biased random walk on a directed rooted labeled
tree. We use these to calculate the speed of a biased random walk on directed rooted labeled trees. The results are mainly
applied to directed trees with recurrent subtrees, where the random walker cannot escape.
Received: 12 March 1997/ In revised form: 11 December 1997 相似文献
6.
We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the
limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation
and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the
regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm.
Received September 30, 2001; in revised form January 8, 2002 相似文献
7.
Symmetric branching random walk on a homogeneous tree exhibits a weak survival phase: For parameter values in a certain interval, the population survives forever with positive probability, but, with probability
one, eventually vacates every finite subset of the tree. In this phase, particle trails must converge to the geometric boundaryΩ of the tree. The random subset Λ of the boundary consisting of all ends of the tree in which the population survives, called
the limit set of the process, is shown to have Hausdorff dimension no larger than one half the Hausdorff dimension of the entire geometric
boundary. Moreover, there is strict inequality at the phase separation point between weak and strong survival except when the branching random walk is isotropic. It is further shown that in all cases there is a distinguished probability measure μ supported by Ω such that the Hausdorff
dimension of Λ∩Ωμ, where Ωμ is the set of μ-generic points of Ω, converges to one half the Hausdorff dimension of Ωμ at the phase separation point. Exact formulas are obtained for the Hausdorff dimensions of Λ and Λ∩Ωμ, and it is shown that the log Hausdorff dimension of Λ has critical exponent 1/2 at the phase separation point.
Received: 30 June 1998 / Revised version: 10 March 1999 相似文献
8.
Summary. Necessary and sufficient conditions for the existence of moments of the first passage time of a random walk S
n
into [x, ∞) for fixed x≧ 0, and the last exit time of the walk from (−∞, x], are given under the condition that S
n
→∞ a.s. The methods, which are quite different from those applied in the previously studied case of a positive mean for the
increments of S
n
, are further developed to obtain the “order of magnitude” as x→∞ of the moments of the first passage and last exit times, when these are finite.
A number of other conditions of interest in renewal theory are also discussed, and some results for the first time for which
the random walk remains above the level x on K consecutive occasions, which has applications in option pricing, are given.
Received: 18 September 1995/In revised form: 28 February 1996 相似文献
9.
Summary. We consider random walks with a bias toward the root on the family tree T of a supercritical Galton–Watson branching process and show that the speed is positive whenever the walk is transient. The
corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary.
When the bias is directed away from the root and the extinction probability is positive, the speed may be zero even though
the walk is transient; the critical bias for positive speed is determined.
Received: 7 July 1995 / In revised form: 9 January 1996 相似文献
10.
Emmanuel Rio 《Probability Theory and Related Fields》2001,119(2):163-175
We propose new concentration inequalities for maxima of set-indexed empirical processes. Our approach is based either on
entropy inequalities or on martingale methods. The improvements we get concern the rate function which is exactly the large
deviations rate function of a binomial law in most of the cases.
Received: 11 January 2000 / Revised version: 12 May 2000 / Published online: 14 December 2000 相似文献
11.
Jérôme Dedecker 《Probability Theory and Related Fields》1998,110(3):397-426
Summary. We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar
to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our
approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides
is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems
for α-mixing or φ-mixing random fields.
Received: 19 February 1997 / In revised form: 2 September 1997 相似文献
12.
Wilfried Buchholz 《Archive for Mathematical Logic》2001,40(4):255-272
Using the concept of notations for infinitary derivations we give an explanation of Takeuti's reduction steps on finite derivations (used in his consistency proof for Π1
1-CA) in terms of the more perspicious infinitary approach from [BS88].
Received: 27 April 1999 / Published online: 21 March 2001 相似文献
13.
B. Anchouche 《manuscripta mathematica》1999,100(4):423-436
We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary
sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank
two over smooth projective varieties of dimension ≥ 2 satisfy the “parabolic” 'Bogomolov inequality
Received: 1 March 1999 / Revised version: 11 June 1999 相似文献
14.
Samuel Grushevsky 《Mathematische Annalen》2001,321(1):1-13
An explicit upper bound for the Weil-Petersson volumes of punctured Riemann surfaces is obtained using Penner's combinatorial
integration scheme from [4]. It is shown that for a fixed number of punctures n and for genus g increasing,
while this limit is exactly equal to two for n=1.
Received: 17 May 2000 / Revised version: 9 August 2000 / Published online: 23 July 2001 相似文献
15.
R. A. Doney 《Probability Theory and Related Fields》1997,107(4):451-465
Summary. If {S
n
,n≧0} is an integer-valued random walk such that S
n
/a
n
converges in distribution to a stable law of index α∈ (0,1) as n→∞, then Gnedenko’s local limit theorem provides a useful estimate for P{S
n
=r} for values of r such that r/a
n
is bounded. The main point of this paper is to show that, under certain circumstances, there is another estimate which is
valid when r/a
n
→ +∞, in other words to establish a large deviation local limit theorem. We also give an asymptotic bound for P{S
n
=r} which is valid under weaker assumptions. This last result is then used in establishing some local versions of generalized
renewal theorems.
Received: 9 August 1995 / In revised form: 29 September 1996 相似文献
16.
David Steinsaltz 《Probability Theory and Related Fields》1997,107(1):99-121
Summary. A self-modifying random walk on is derived from an ordinary random walk on the integers by interpolating a new vertex into each edge as it is crossed. This
process converges almost surely to a random variable which is totally singular with respect to Lebesgue measure, and which
is supported on a subset of having Hausdorff dimension less than , which we calculate by a theorem of Billingsley. By generating function techniques we then calculate the exponential rate
of convergence of the process to its limit point, which may be taken as a bound for the convergence of the measure in the
Wasserstein metric. We describe how the process may viewed as a random walk on the space of monotone piecewise linear functions,
where moves are taken by successive compositions with a randomly chosen such function.
Received: 20 November 1995 / In revised form: 14 May 1996 相似文献
17.
Nakahiro Yoshida 《Probability Theory and Related Fields》1997,109(3):301-342
Summary. We present an asymptotic expansion of the distribution of a random variable which admits a stochastic expansion around a
continuous martingale. The emphasis is put on the use of the Malliavin calculus; the uniform nondegeneracy of the Malliavin
covariance under certain truncation plays an essential role as the Cramér condition did in the case of independent observations.
Applications to statistics are presented.
Received: 5 September 1995 / In revised form: 20 October 1996 相似文献
18.
We prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or Euclidean
space, under approximate additivity and regularity hypotheses. The rate function is the convex dual of the limiting logarithmic
moment generating function. In some applications the rate function can be expressed in terms of relative entropy. The general
result applies to processes in Euclidean combinatorial optimization, statistical mechanics, and computational geometry. Examples
include the length of the minimal tour (the traveling salesman problem), the length of the minimal matching graph, the length
of the minimal spanning tree, the length of the k-nearest neighbors graph, and the free energy of a short-range spin glass model.
Received: 3 April 1999 / Revised version: 23 June 1999 / Published online: 8 May 2001 相似文献
19.
20.
Jan von Plato 《Archive for Mathematical Logic》2001,40(7):541-567
The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with
twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination
rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases.
Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.
Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening or contraction formulas remain in Γ, a correspondence with the formal derivability relation of natural
deduction is obtained: All formulas of Γ become open assumptions in natural deduction, through an inductively defined translation.
Weakenings are interpreted as vacuous discharges, and contractions as multiple discharges. In the other direction, non-normal
derivations translate into derivations with cuts having the cut formula principal either in both premisses or in the right
premiss only.
Received: 1 December 1998 / Revised version: 30 June 2000 / Published online: 18 July 2001 相似文献