Search Results

We study the natural question of constructing pseudorandom generators (PRGs) for low-degree polynomial threshold functions (PTFs). We give a PRG with seed length $\log n/\epsilon^{O(d)}$ fooling degree $d$ PTFs with error at most $\epsilon$. Previously, no ...

Let X be randomly chosen from {-1,1}ⁿ, and let Y be randomly chosen from the standard spherical Gaussian on Rⁿ. For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that |Pr[X ∈ P] - Pr[Y ∈ P]| ≤ log^8/5k • Δ, ...

We study the natural question of constructing pseudorandom generators (PRGs) for low-degree polynomial threshold functions (PTFs). We give a PRG with seed-length log n/ε^O(d) fooling degree d PTFs with error at most ε. Previously, no nontrivial ...

We study the multidimensional reflection map on the spaces D([0, T], ℝ^k) and D([0, ∞), ℝ^k) of right-continuous ℝ^k-valued functions on [0, T] or [0, ∞) with left limits, endowed with variants of the Skorohod (1956) M₁ topology. The reflection map was used ...

We review functional central limit theorems (FCLTs) for the queue-content process in a single-server queue with finite waiting room and the first-come first-served service discipline. We emphasize alternatives to the familiar heavy-traffic FCLTs with ...

The Byrnes--Martin integral invariance principle for ordinary differential equations is extended to differential inclusions on {Bbb R}^N. The extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a ...

Many useful descriptions of stochastic models can be obtained from functional limit theorems invariance principles or weak convergence theorems for probability measures on function spaces. These descriptions typically come from standard functional limit ...