Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From $1$ to $6$: a finer analysis of perturbed branching Brownian motion   The logarithmic correction for the order of the maximum for two-speed
branching Brownian motion changes discontinuously when approaching slopes
$\sigma_1^2=\sigma_2^2=1$ which corresponds to standard branching Brownian
motion. In this article we study this transition more closely by choosing
$\sigma_1^2=1\pm t^{-\alpha}$ and $\sigma_2^2=1\pm t^{-\alpha}$. We show that
the logarithmic correction for the order of the maximum now smoothly
interpolates between the correction in the iid case $\frac{1}{2\sqrt
2}\ln(t),\;\frac{3}{2\sqrt 2}\ln(t)$ and $\frac{6}{2\sqrt 2}\ln(t)$ when
$0<\alpha<\frac{1}{2}$. This is due to the localisation of extremal particles
at the time of speed change which depends on $\alpha$ and differs from the one
in standard branching Brownian motion. We also establish in all cases the
asymptotic law of the maximum and characterise the extremal process, which
turns out to coincide essentially with that of standard branching Brownian
motion.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom