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The local behavior of typical solutions of random constraint satisfaction problems (csp) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the constraint ...

Trickle-down is a phenomenon in high-dimensional expanders with many important applications — for example, it is a key ingredient in various constructions of high-dimensional expanders or the proof of rapid mixing for the basis exchange walk on matroids ...

A random m× n matrix S is an oblivious subspace embedding (OSE) with parameters є>0, δ∈(0,1/3) and d≤ m≤ n, if for any d-dimensional subspace W⊆ Rⁿ, P( ∀_{x∈ W} (1+є)⁻¹||x||≤ ||Sx||≤ (1+є)||x|| )≥ 1−δ. It is known that the embedding dimension of an OSE must ...

We give a stochastic optimization algorithm that solves a dense n× n real-valued linear system Ax=b, returning x such that ||Ax−b||≤ є||b|| in time: Õ((n²+nk^ω−1)log1/є), where k is the number of singular values of A larger than O(1) times its smallest ...

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression, p-norm regression (...