We prove that Ising models on the hypercube with general quadratic interactions satisfy a
Poincaré inequality with respect to the natural Dirichlet form corresponding to Glauber …

Abstract An (n, d, λ)-graph is ad regular graph on n vertices in which the absolute value of
any nontrivial eigenvalue is at most λ. For any constant d≥ 3, ϵ> 0 and all sufficiently large …

This is a survey of unconditional pseudorandom generators (PRGs). A PRG uses a short,
truly random seed to generate a long," pseudorandom" sequence of bits. To be more …

We give a strongly explicit construction of ϵ approximate k-designs for the orthogonal group
O (N) and the unitary group U (N), for N=2^n. Our designs are of cardinality poly(N^k/ϵ) …

Combinatorial reconfiguration is an emerging field of theoretical computer science that
studies the reachability between a pair of feasible solutions for a particular combinatorial …

Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type
characterization of PSPACE, which we call a probabilistically checkable reconfiguration …

Consider a random geometric 2-dimensional simplicial complex X sampled as follows: first,
sample n vectors u 1,…, un uniformly at random on S d− 1; then, for each triple i, j, k∈[n] …

In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time
auxiliary classical computation, we construct a fault tolerance protocol with constant-space …

Classical locally recoverable codes, which permit highly efficient recovery from localized
errors as well as global recovery from larger errors, provide some of the most useful codes …

We propose a new, efficiently solvable hierarchy of semidefinite programming relaxations for
inference problems. As test cases, we consider the problem of community detection in block …