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Showing 1 to 3 of 3 for “"Rademacher sums"”.
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Games on Graphs and Other Combinatorial Problems
… progress on some questions in the settings of Rademacher sums and graph theory. In Chapter 2, we study the $(m,b)$ Maker-Breaker percolation game. This game, played by two players on the square lattice, was introduced by Day and Falgas-Ravry. The outcome of this game depends crucially on the …
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Topics in Probabilistic Combinatorics
… x)$, where $X=\sum_{i=1}^n a_i\epsilon_i$ is a Rademacher sum; $a_i$ are positive constants normalised so that $\sum_{i=1}^n a_i^2 = 1$, and $\epsilon_i$ are independent and uniform signs $\pm 1$. We determine the value of $\inf_X \mathbb{P}(|X| \geq x)$ for all values $x\geq 0$, confirming a …
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Extremal, Probabilistic, and Infinitary Problems in Combinatorics
… abstract of a series of results centred around Rademacher sums. The object of interest is P(Σ_(i=1)^n ξ_i v_i ∈ S), where ξ_i are independent random variables sampled uniformly on {−1, +1}, each v_i is a vector in R^d for some fixed d, and S is some set. We first consider anti-concentration …