\u2113_p(n) sphere family

The collection of high-dimensional spheres defined by the \u2113_p norm for 1 \u2264 p \u2264 \u221e, each with the radius convention used in the abstract.

• Types

  geometric family, sampling space

• Aliases

  lp sphere family, \u2113_p sphere

• Contributors
  박진우 (dztg5apj7m) extractionB (s683577b42) reviewsijun-yang (m6hj47gh7t) review

• Asymptotic Distribution of Coordinates on High Dimensional Spheres

  35 citations

• For the full family of \u2113_p(n) spheres with 1 \u2264 p \u2264 \u221e, the coordinate distribution converges at rate \u221an and is described by weak convergence of a normalized empirical process to a limiting Gaussian process built from a Brownian bridge and a simple normal process.

• No direct concept-to-concept edges are published yet.

• \u21132(n) sphere

  geometric object, sampling space1 shared papers
• \u21131(n) sphere

  geometric object, sampling space1 shared papers
• double exponential distribution

  probability distribution1 shared papers
• normal distribution

  probability distribution1 shared papers
• normalized empirical process

  stochastic process, asymptotic object1 shared papers
• brownian bridge

  stochastic process, gaussian process1 shared papers
• simple normal process

  stochastic process, gaussian process1 shared papers
• weak convergence

  probability concept, limit notion1 shared papers