9,513 research outputs found
Invariance principle on the slice
We prove an invariance principle for functions on a slice of the Boolean
cube, which is the set of all vectors {0,1}^n with Hamming weight k. Our
invariance principle shows that a low-degree, low-influence function has
similar distributions on the slice, on the entire Boolean cube, and on Gaussian
space.
Our proof relies on a combination of ideas from analysis and probability,
algebra and combinatorics.
Our result imply a version of majority is stablest for functions on the
slice, a version of Bourgain's tail bound, and a version of the Kindler-Safra
theorem. As a corollary of the Kindler-Safra theorem, we prove a stability
result of Wilson's theorem for t-intersecting families of sets, improving on a
result of Friedgut.Comment: 36 page
Invariance principle via orthomartingale approximation
We obtain a necessary and sufficient condition for the
orthomartingale-coboundary decomposition. We establish a sufficient condition
for the approximation of the partial sums of a strictly stationary random
fields by those of stationary orthomartingale differences. This condition can
be checked under multidimensional analogues of the Hannan condition and the
Maxwell-Woodroofe condition
Invariance principle for stochastic processes with short memory
In this paper we give simple sufficient conditions for linear type processes
with short memory that imply the invariance principle. Various examples
including projective criterion are considered as applications. In particular,
we treat the weak invariance principle for partial sums of linear processes
with short memory. We prove that whenever the partial sums of innovations
satisfy the --invariance principle, then so does the partial sums of its
corresponding linear process.Comment: Published at http://dx.doi.org/10.1214/074921706000000734 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Almost sure functional central limit theorem for non-nestling random walk in random environment
We consider a non-nestling random walk in a product random environment. We
assume an exponential moment for the step of the walk, uniformly in the
environment. We prove an invariance principle (functional central limit
theorem) under almost every environment for the centered and diffusively scaled
walk. The main point behind the invariance principle is that the quenched mean
of the walk behaves subdiffusively.Comment: 54 pages. Small edits in tex
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