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Partially Observed Boolean Sequences and Noise Sensitivity
| Content Provider | Scilit |
|---|---|
| Author | Ahlberg, Daniel |
| Copyright Year | 2014 |
| Description | Let ${\mathcal H}$ denote a collection of subsets of {1,2,. . .,n}, and assign independent random variables uniformly distributed over [0,1] to the n elements. Declare an element p-present if its corresponding value is at most p. In this paper, we quantify how much the observation of the r-present (r>p) set of elements affects the probability that the set of p-present elements is contained in ${\mathcal H}$ . In the context of percolation, we find that this question is closely linked to the near-critical regime. As a consequence, we show that for every r>1/2, bond percolation on the subgraph of the square lattice given by the set of r-present edges is almost surely noise sensitive at criticality, thus generalizing a result due to Benjamini, Kalai and Schramm. |
| Related Links | http://arxiv.org/pdf/1308.2656 http://arxiv.org/abs/1308.2656 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F9259F2EDD3173FB231E0A837A5FD9AF/S0963548314000030a.pdf/div-class-title-partially-observed-boolean-sequences-and-noise-sensitivity-div.pdf |
| Ending Page | 330 |
| Page Count | 14 |
| Starting Page | 317 |
| ISSN | 09635483 |
| e-ISSN | 14692163 |
| DOI | 10.1017/s0963548314000030 |
| Journal | Combinatorics, Probability and Computing |
| Issue Number | 3 |
| Volume Number | 23 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2014-05-01 |
| Access Restriction | Open |
| Subject Keyword | Combinatorics, Probability and Computing Primary 60c05 Secondary 60k35 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics |
