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A note on general sliding window processes


 
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1. Title Title of document A note on general sliding window processes
 
2. Creator Author's name, affiliation, country Noga Alon; Tel Aviv University; Israel
 
2. Creator Author's name, affiliation, country Ohad Noy Feldheim; Weizmann Institute of Sciences; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) k-factor, d-dependent, de Bruijn, Ramsey
 
3. Subject Subject classification 60G07, 60C05
 
4. Description Abstract Let $f:\mathbb{R}^k\to\mathbb{R}$ be a measurable function, and let ${(U_i)}_{i\in\mathbb{N}}$ be a sequence of i.i.d. random variables. Consider the random process $Z_i=f(U_{i},...,U_{i+k-1})$. We show that for all $\ell$, there is a positive probability, uniform in $f$, for $Z_1,...,Z_\ell$ to be monotone. We give upper and lower bounds for this probability, and draw corollaries for $k$-block factor processes with a finite range. The proof is based on an application of combinatorial results from Ramsey theory to the realm of continuous probability.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) USA-Israeli BSF grant, ISF grant, Hermann Minkowski Minerva Center for Geometry at Tel Aviv University,the Israeli I-Core program, Israel Science Foundation.
 
7. Date (YYYY-MM-DD) 2014-09-22
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/3341
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3341
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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