Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical results for the distribution of first hitting times of random
  walks on random regular graphs   We present analytical results for the distribution of first hitting times of
random walks (RWs) on random regular graphs (RRGs) of degree $c \ge 3$ and a
finite size $N$. Starting from a random initial node at time $t=1$, at each
time step $t \ge 2$ an RW hops randomly into one of the $c$ neighbors of its
previous node. In some of the time steps the RW may hop into a yet-unvisited
node while in other time steps it may revisit a node that has already been
visited before. The first time at which the RW enters a node that has already
been visited before is called the first hitting time or the first intersection
length. The first hitting event may take place either by backtracking (BT) to
the previous node or by retracing (RET), namely stepping into a node which has
been visited two or more time steps earlier. We calculate the tail distribution
$P( T_{\rm FH} > t )$ of first hitting (FH) times as well as its mean $\langle
T_{\rm FH} \rangle$ and variance ${\rm Var}(T_{\rm FH})$. We also calculate the
probabilities $P_{\rm BT}$ and $P_{\rm RET}$ that the first hitting event will
occur via the backtracking scenario or via the retracing scenario,
respectively. We show that in dilute networks the dominant first hitting
scenario is backtracking while in dense networks the dominant scenario is
retracing and calculate the conditional distributions $P(T_{\rm FH}=t| {\rm
BT})$ and $P(T_{\rm FH}=t| {\rm RET})$, for the two scenarios. The analytical
results are in excellent agreement with the results obtained from computer
simulations. Considering the first hitting event as a termination mechanism of
the RW trajectories, these results provide useful insight into the general
problem of survival analysis and the statistics of mortality rates when two or
more termination scenarios coexist.

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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn