Isoperimetric Inequalities Made Simpler
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912493798948864 |
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| author | Eldan, Ronen Kindler, Guy Lifshitz, Noam Minzer, Dor |
| author_facet | Eldan, Ronen Kindler, Guy Lifshitz, Noam Minzer, Dor |
| contents | We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show:
1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result conjectured by Talagrand and recently proved by Eldan and Gross.
2. A strengthening of the Friedgut junta theorem, asserting that if the $p$-moment of the sensitivity of a function is constant for some $1/2 + \varepsilon\leq p\leq 1$, then the function is close to a junta. In this language, Friedgut's theorem is the special case that $p=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06686 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Isoperimetric Inequalities Made Simpler Eldan, Ronen Kindler, Guy Lifshitz, Noam Minzer, Dor Combinatorics Discrete Mathematics We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show: 1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result conjectured by Talagrand and recently proved by Eldan and Gross. 2. A strengthening of the Friedgut junta theorem, asserting that if the $p$-moment of the sensitivity of a function is constant for some $1/2 + \varepsilon\leq p\leq 1$, then the function is close to a junta. In this language, Friedgut's theorem is the special case that $p=1$. |
| title | Isoperimetric Inequalities Made Simpler |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2204.06686 |