... asymptotics
for the number of steps needed by simple random walk in Z
2
to cover the disc
of radius n.
1. Introduction
In this paper, we introduce a unified method for analyzing cover times
for random walks ...
Cover times for Brownian
motionand random walks
in two dimensions
By Amir Dembo, Yuval Peres, Jay Rosen, and Ofer
Zeitouni
Annals of M...
... constraints. He has published in the
following topics: database design, database constraints, document indexing, and
information science. He is a member of the Association for Computing Machinery ... Knowledge Engineering 50 (2004) 175–194
[12] M.F. van Bommel, T.J. Beck, Incremental encoding of multiple inheritance
hierarchies supporting lattice operations, Linkoping Electronic Artic...
... returning symmetric open
intervals containing the critical point ζ then ζ is periodic.
Proof. Let J be the interior of the intersection of all regularly returning
symmetric open intervals containing ... into two cases depending on whether ω(ζ) intersects
the domains of finitely many branches of F , or in nitely many.
The case with in nitely many branches. For each domain ∆ of a branch
wh...
... \ Sing(S) is comfortably embedded into
M, and that f is tangential to S with ν
f
> 1.LetSing(S)∪Sing(X
f
)=
λ
Σ
λ
be the decomposition of Sing(S) ∪ Sing(X
f
) in connected components. Finally,
let ... map. Then:
(i) if S is comfortably embedded in M then E
S
is comfortably embedded
in M
S
, and the choice of a splitting morphism for S induces a splitting
morphism for E
S
;
(ii)...
... They
are grateful to C. Thiele for his inspirational work [10] and for some help-
ful remarks. They also thank the referee for pointing out an oversight in a
construction in the first version of this ... C2
−ηµ
2
−
µ
p
j
|I
T
|
1
2
.
UNIFORM BOUNDS FOR THE BILINEAR HILBERT TRANSFORMS, I
901
identifying trees with sets of pairs of integers, we will use this identification
throughout....
... measurable set in the set of in nite trajectories.
Since Γ contains at least two distinct elements, Lemma 4.2 and Lemma
4.3 imply that
0 <ν
∞
(A) < 1.
It is clear that if two trajectories coincide ... this map stabilizes
pointwise along in nite trajectories of the random walk. (We know this for each
point, and since ∆ is countable it implies that this happens for all the p...
... Γ
0
(N)-invariant partial
modular symbol
m
α
{r → s} :=
1
2πi
s
r
dlog α.(40)
Dedekind sums. The line integrals in (40) defining the modular symbol
m
α
can be expressed in terms of classical Dedekind ... notation in designating the integrand in the same
way. However this notation is suggestive, and should result in no confusion
since double integral signs are always used to describ...
... −1
O
k
.
Since the left-hand side of this inequality is less than or equal to α
2
, the lemma
follows.
Completion of the Main Lemma in the type II case. In the following, we
distinguish two cases. In ... there exist an interval I which contains the critical point 0 in its interior,
and a positive integer s>1, such that the intervals I,f(I), ··· ,f
s−1
(I) have
pairwise disjoint i...
... special point in
[u, u + 1]). Note that |E(w)|≥|E(x)| + O(z
−u
) for any x ≥ u.IfE(x)
maintains the same sign for all x ≥ w set v = ∞; otherwise let v denote the
in mum of those points x ≥ w for which ... like
random numbers chosen with probability φ(q)/q. Indeed when φ(q)/q → 0
AN UNCERTAINTY PRINCIPLE FOR ARITHMETIC SEQUENCES
595
(meaning that the subset is poorly distributed...
... mixing had been proved for in nitely many combinatorics),
WEAK MIXING FOR INTERVAL EXCHANGE TRANSFORMATIONS
641
1.3. Outline. We start this paper with basic background on cocycles
over expanding ... mixing transformation
is weakly mixing and every weakly mixing transformation is ergodic. A clas-
sical theorem states that any invertible measure-preserving transformation f
is weakly mixing...