Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical properties of avalanches via the c-record process   We study the statistics of avalanches, as a response to an applied force,
undergone by a particle hopping on a one dimensional lattice where the pinning
forces at each site are independent and identically distributed (I.I.D), each
drawn from a continuous $f(x)$. The avalanches in this model correspond to the
inter-record intervals in a modified record process of I.I.D variables, defined
by a single parameter $c>0$. This parameter characterizes the record formation
via the recursive process $R_k > R_{k-1}-c$, where $R_k$ denotes the value of
the $k$-th record. We show that for $c>0$, if $f(x)$ decays slower than an
exponential for large $x$, the record process is nonstationary as in the
standard $c=0$ case. In contrast, if $f(x)$ has a faster than exponential tail,
the record process becomes stationary and the avalanche size distribution
$\pi(n)$ has a decay faster than $1/n^2$ for large $n$. The marginal case where
$f(x)$ decays exponentially for large $x$ exhibits a phase transition from a
non-stationary phase to a stationary phase as $c$ increases through a critical
value $c_{\rm crit}$. Focusing on $f(x)=e^{-x}$ (with $x\ge 0$), we show that
$c_{\rm crit}=1$ and for $c<1$, the record statistics is non-stationary.
However, for $c>1$, the record statistics is stationary with avalanche size
distribution $\pi(n)\sim n^{-1-\lambda(c)}$ for large $n$. Consequently, for
$c>1$, the mean number of records up to $N$ steps grows algebraically $\sim
N^{\lambda(c)}$ for large $N$. Remarkably, the exponent $\lambda(c)$ depends
continously on $c$ for $c>1$ and is given by the unique positive root of
$c=-\ln (1-\lambda)/\lambda$. We also unveil the presence of nontrivial
correlations between avalanches in the stationary phase that resemble
earthquake sequences.

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The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin