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We prove that in every bipartite Cayley graph of every non-amenable group, there is a perfect matching that is obtained as a factor of independent uniform random variables. We also discuss expansion properties of factors and improve the Hoffman spectral bound on independence number of finite graphs. A perfect matching in a graph is a set of its edges that… (More)

Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems (or more generally power-law systems) are very common in chemistry, biology, and engineering, and are often used to… (More)

Background Joint work with Fedor Nazarov and Igor Verbitsky (preprint) Start with general functional analysis theorem: Background Joint work with Fedor Nazarov and Igor Verbitsky (preprint) Start with general functional analysis theorem: Given an integral operator T on a σ-finite measure space (Ω, ω) with kernel K : Background Joint work with Fedor Nazarov… (More)

In the trace reconstruction problem, an unknown bit string x ∈ {0, 1} n is observed through the deletion channel, which deletes each bit of x with some constant probability q, yielding a contracted string x. How many independent copies of x are needed to reconstruct x with high probability? Prior to this work, the best upper bound, due to Holenstein,… (More)

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