All reports by Author Arturs Backurs:

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TR13-039
| 18th March 2013
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Arturs Backurs, Mohammad Bavarian#### On the sum of $L1$ influences

Revisions: 2

Arturs Backurs, Mohammad Bavarian

For a multilinear polynomial $p(x_1,...x_n)$, over the reals, the $L1$-influence is defined to be $\sum_{i=1}^n E_x\left[\frac{|p(x)-p(x^i)|}{2} \right]$, where $x^i$ is $x$ with $i$-th bit swapped. If $p$ maps $\{-1,1\}^n$ to $[-1,1]$, we prove that the $L1$-influence of $p$ is upper bounded by a function of its degree (and independent of ... more >>>