License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2022.101
URN: urn:nbn:de:0030-drops-156975
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Liu, Yang P. ; Sah, Ashwin ; Sawhney, Mehtaab

A Gaussian Fixed Point Random Walk

LIPIcs-ITCS-2022-101.pdf (0.7 MB)


In this note, we design a discrete random walk on the real line which takes steps 0,±1 (and one with steps in {±1,2}) where at least 96% of the signs are ±1 in expectation, and which has 𝒩(0,1) as a stationary distribution. As an immediate corollary, we obtain an online version of Banaszczyk’s discrepancy result for partial colorings and ±1,2 signings. Additionally, we recover linear time algorithms for logarithmic bounds for the Komlós conjecture in an oblivious online setting.

BibTeX - Entry

  author =	{Liu, Yang P. and Sah, Ashwin and Sawhney, Mehtaab},
  title =	{{A Gaussian Fixed Point Random Walk}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{101:1--101:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-156975},
  doi =		{10.4230/LIPIcs.ITCS.2022.101},
  annote =	{Keywords: Discrepancy, Partial Coloring}

Keywords: Discrepancy, Partial Coloring
Collection: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)
Issue Date: 2022
Date of publication: 25.01.2022

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