Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-intersection local times of random walks: Exponential moments in
  subcritical dimensions   Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold
self-intersection local time of a simple random walk on the lattice $\Z^d$ up
to time $t$. This is the $p$-norm of the vector of the walker's local times,
$\ell_t$. We derive precise logarithmic asymptotics of the expectation of
$\exp\{\theta_t \|\ell_t\|_p\}$ for scales $\theta_t>0$ that are bounded from
above, possibly tending to zero. The speed is identified in terms of mixed
powers of $t$ and $\theta_t$, and the precise rate is characterized in terms of
a variational formula, which is in close connection to the {\it
Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation
principle for $\|\ell_t\|_p/(t r_t)$ for deviation functions $r_t$ satisfying
$t r_t\gg\E[\|\ell_t\|_p]$. Informally, it turns out that the random walk
homogeneously squeezes in a $t$-dependent box with diameter of order $\ll
t^{1/d}$ to produce the required amount of self-intersections. Our main tool is
an upper bound for the joint density of the local times of the walk.

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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg