Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-size scaling analysis of binary stochastic processes and
  universality classes of information cascade phase transition   We propose a finite-size scaling analysis of binary stochastic processes
$X(t)\in \{0,1\}$ based on the second moment correlation length $\xi$ for the
autocorrelation function $C(t)$. The purpose is to clarify the critical
properties and provide a new data analysis method for information cascades. As
a simple model to represent the different behaviors of subjects in information
cascade experiments, we assume that $X(t)$ is a mixture of an independent
random variable that takes 1 with probability $q$ and a random variable that
depends on the ratio $z$ of the variables taking 1 among recent $r$ variables.
We consider two types of the probability $f(z)$ that the latter takes 1: (i)
analog [$f(z)=z$] and (ii) digital [$f(z)=\theta(z-1/2)$]. We study the
universal functions of scaling for $\xi$ and the integrated correlation time
$\tau$. For finite $r$, $C(t)$ decays exponentially as a function of $t$, and
there is only one stable renormalization group (RG) fixed point. In the limit
$r\to \infty$, where $X(t)$ depends on all the previous variables, $C(t)$ in
model (i) obeys a power law, and the system becomes scale invariant. In model
(ii) with $q\neq 1/2$, there are two stable RG fixed points, which correspond
to the ordered and disordered phases of the information cascade phase
transition with critical exponents $\beta=1$ and $\nu_{||}=2$.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas