---
res:
  bibo_abstract:
  - "We study simple dynamics in the population protocol model, in\r\nwhich \U0001D45B
    agents start with totally ordered initial opinions \U0001D4651, \U0001D4652, .
    . . ,\r\n\U0001D465\U0001D45B and, in each round, a randomly chosen agent changes
    its opinion\r\nas a function of the opinion of other randomly chosen agents. Such\r\ndynamics
    often converge to consensus on a single fixation value \U0001D44Bˆ.\r\nThis paper
    asks how to control the distribution of \U0001D44Bˆ as a randomised\r\nchoice
    among the initial opinions by designing suitable simple\r\ndynamics. Writing the
    sorted initial values as \U0001D465(1) ≤ · · · ≤ \U0001D465(\U0001D45B)\r\n,\r\nwe
    design two protocols that realise natural target laws over order\r\nstatistics.\r\nFirst,
    for a parameter \U0001D45D ∈ (0, 1), our geometric protocol biases\r\ntoward larger
    opinions and satisfies P\r\n\r\n\U0001D44Bˆ = \U0001D465(\U0001D458)\r\n\r\n∝
    \U0001D45D\r\n\U0001D45B−\U0001D458\r\n, for\r\n\U0001D458 = 1, . . . , \U0001D45B.
    Equivalently, P\r\n\r\n\U0001D44Bˆ = \U0001D465(\U0001D458)\r\n\r\n= (1 − \U0001D45D)\U0001D45D\r\n\U0001D45B−\U0001D458\r\n/(1
    − \U0001D45D\r\n\U0001D45B\r\n).\r\nSecond, our binomial protocol assigns a shifted
    binomial law to the\r\nranks in ascending order: if \U0001D43E −1 ∼ Bin(\U0001D45B−1,
    1−\U0001D45D), then \U0001D44Bˆ = \U0001D465(\U0001D43E)\r\n,\r\ni.e., P\r\n\r\n\U0001D44Bˆ
    = \U0001D465(\U0001D458)\r\n\r\n=\r\n\U0001D45B−1\r\n\U0001D458−1\r\n\x01\r\n\U0001D45D\r\n\U0001D45B−\U0001D458\r\n(1
    − \U0001D45D)\r\n\U0001D458−1\r\n, for \U0001D458 = 1, . . . , \U0001D45B.\r\nApplications
    of this include computing the Top-\U0001D458 values for\r\nsmall \U0001D458 on
    general interaction graphs. A central contribution of\r\nthis work is that, in
    contrast to most population protocols, we can\r\ncharacterise the fixation distribution
    in closed form. This is enabled\r\nby a novel analysis technique, which also yields
    applications: we\r\nderive new results for the Median protocol that extend the
    state of\r\nthe art.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Niccolò
      foaf_name: D'Archivio, Niccolò
      foaf_surname: D'Archivio
  - foaf_Person:
      foaf_givenName: Hind
      foaf_name: Almahmoud, Hind
      foaf_surname: Almahmoud
  - foaf_Person:
      foaf_givenName: Emanuele
      foaf_name: Natale, Emanuele
      foaf_surname: Natale
  - foaf_Person:
      foaf_givenName: Frederik
      foaf_name: Mallmann-Trenn, Frederik
      foaf_surname: Mallmann-Trenn
      foaf_workInfoHomepage: http://www.librecat.org/personId=68748c44-84d5-11f1-b4f6-ca083374e553
  bibo_doi: 10.1145/3796701.3815922
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/9798400725128
  dct_language: eng
  dct_publisher: Association for Computing Machinery@
  dct_title: Order statistics in population protocols via simple dynamics@
...