Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maxima of Two Random Walks: Universal Statistics of Lead Changes   We investigate statistics of lead changes of the maxima of two discrete-time
random walks in one dimension. We show that the average number of lead changes
grows as $\pi^{-1}\ln(t)$ in the long-time limit. We present theoretical and
numerical evidence that this asymptotic behavior is universal. Specifically,
this behavior is independent of the jump distribution: the same asymptotic
underlies standard Brownian motion and symmetric Levy flights. We also show
that the probability to have at most n lead changes behaves as $t^{-1/4}[\ln
t]^n$ for Brownian motion and as $t^{-\beta(\mu)}[\ln t]^n$ for symmetric Levy
flights with index $\mu$. The decay exponent $\beta(\mu)$ varies continuously
with the Levy index when $0<\mu<2$, while $\beta=1/4$ for $\mu>2$.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas