Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The naming game in language dynamics revisited   This article studies a biased version of the naming game in which players
located on a connected graph interact through successive conversations to
bootstrap a common name for a given object. Initially, all the players use the
same word B except for one bilingual individual who also uses word A. Both
words are attributed a fitness, which measures how often players speak
depending on the words they use and how often each word is pronounced by
bilingual individuals. The limiting behavior depends on a single parameter: phi
= the ratio of the fitness of word A to the fitness of word B. The main
objective is to determine whether word A can invade the system and become the
new linguistic convention. In the mean-field approximation, invasion of word A
is successful if and only if phi > 3, a result that we also prove for the
process on complete graphs relying on the optimal stopping theorem for
supermartingales and random walk estimates. In contrast, for the process on the
one-dimensional lattice, word A can invade the system whenever phi > 1.053
indicating that the probability of invasion and the critical value for phi
strongly depend on the degree of the graph. The system on regular lattices in
higher dimensions is also studied by comparing the process with percolation
models.

28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess