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ON THE STRONG LAW OF LARGE NUMBERS
N lim 1( 1: f(nkx)) = 0, N-N k_l or roughly speaking the strong law of large numbers holds for f(nkx) (in fact the authors prove that Ef(nkx)/k converges almost everywhere) . The question was raisedExpand
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On the Complexity of Random Satisfiability Problems with Planted Solutions
TLDR
The problem of identifying a planted assignment given a random k-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution can always be identified given a formula with O(n log n) clauses. Expand
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Spectral thresholds in the bipartite stochastic block model
TLDR
We consider a bipartite stochastic block model on vertex sets $ V_1$ and $V_2$, with planted partitions in each, and ask at what densities efficient algorithms can recover the partition of the smaller vertex set. Expand
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Subsampled Power Iteration: a Unified Algorithm for Block Models and Planted CSP's
TLDR
We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems (CSP), via a common generalization in terms of random bipartite graphs. Expand
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Algorithms for #BIS-hard problems on expander graphs
TLDR
We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model in the non-uniqueness regime of the infinite $\Delta$-regular tree. Expand
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On kissing numbers and spherical codes in high dimensions
We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on the kissing number in dimension $d$. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor inExpand
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The Bohman-Frieze process near criticality
TLDR
We present several new results on the phase transition of the Bohman-Frieze random graph process, a simple modification of the Erd\H{o}s-R\'{e}nyi process. Expand
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On the average size of independent sets in triangle-free graphs
We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$, showing that an independent set drawn uniformlyExpand
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Counting independent sets in cubic graphs of given girth
TLDR
We prove a tight upper bound on the independence polynomial (and total number of independent sets) of cubic graphs of girth at least 5. Expand
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Independent sets, matchings, and occupancy fractions
TLDR
We prove tight upper bounds on the logarithmic derivative of the independence and matching polynomials of d-regular graphs and prove the asymptotic upper matching conjecture of Friedland, Krop, Lundow, and Markstrom. Expand
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