Related papers: Asymptotics for the partition function in two-cut …

In this paper, we first establish asymptotic expansions of the Humbert function $\Psi_1$ for one large variable. The resulting expansions are then used to derive an asymptotic expansion of Saran's hypergeometric function $F_K$ when two of…

Let $B_s$ be a $d$-dimensional Brownian motion and $\omega(dx)$ be an independent Poisson field on $\mathbb{R}^d$. The almost sure asymptotics for the logarithmic moment generating function [\log\math…

We provide a general framework for proving asymptotic equidistribution, convexity, and log concavity of coefficients of generating functions on arithmetic progressions. Our central tool is a variant of Wright's Circle Method proved by two…

Let $\{e_j\}$ be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold $(M,g)$. Let $H \subset M$ be a submanifold and let $\{\psi_k\}$ be an orthonormal basis of Laplace eigenfunctions of $H$ with the induced…

The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The…

We consider classical $O(N)$ vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We prove that such expansions define asymptotic series, and derive…

We consider expectations of the form $E [tr h_1(X_1^N)... tr h_r(X_r^N)]$, where $X_i^N$ are self-adjoint polynomials in various independent classical random matrices and $h_i$ are smooth test function and obtain a large $N$ expansion of…

We study asymptotics of the dimer model on large toric graphs. Let $\mathbb L$ be a weighted $\mathbb{Z}^2$-periodic planar graph, and let $\mathbb{Z}^2 E$ be a large-index sublattice of $\mathbb{Z}^2$. For $\mathbb L$ bipartite we show…

We consider the V-A Fermi interaction and apply an earlier developed method for summing up the leading asymptotics for scattering amplitudes in non-renormalizable theories. We consider the amplitude of fermion-antifermion scattering and…

For a subset $\mathcal A\subset \mathbb N$, let $p_{\mathcal A}(n)$ denote the restricted partition function which counts partitions of $n$ with all parts lying in $\mathcal A$. In this paper, we use a variation of the Hardy-Littlewood…

We study expected values of the polynomials $P_N^{}(z)=\prod_{1\leq n\leq N}(X_n^2+z^2)$ whose $2N$ zeros $\{\pm i X_k\}^{}_{k=1,...,N}$ are generated by $N$ identically distributed multi-variate mean-zero normal random variables…

Following the ideas of Rosenbloom [7] and Hayman [5], Luis B\'aez-Duarte gives in [1] a probabilistic proof of Hardy-Ramanujan's asymptotic formula for the partitions of an integer. The main principle of the method relies on the convergence…

We study the characteristic polynomial $p_{n}(x)=\prod_{j=1}^{n}(|z_{j}|-x)$ where the $z_{j}$ are drawn from the Mittag-Leffler ensemble, i.e. a two-dimensional determinantal point process which generalizes the Ginibre point process. We…

We use a semi-Markov process method to calculate large deviations of counting statistics for three open quantum systems, including a resonant two-level system and resonant three-level systems in the $\Lambda$- and $V$-configurations. In the…

Recently presented explicit formulae for asymptotic expansions of Feynman diagrams in the Sudakov limit are applied to typical two-loop diagrams. For a diagram with one non-zero mass these formulae provide an algorithm for analytical…

We consider the discrete spectrum of the two-dimensional Hamiltonian $H=H_0+V$, where $H_0$ is a Schr\"odinger operator with a non-constant magnetic field $B$ that depends only on one of the spatial variables, and $V$ is an electric…

Simple asymptotic expansions for the Jacobi functions $P_\nu^{(\alpha, \beta)}(z)$ and $Q_\nu^{(\alpha, \beta)}(z)$ for large degree $\nu$, with fixed parameters $\alpha$ and $\beta$, are surprisingly rare in the literature, with only a few…

We consider unitary ensembles of Hermitian NxN matrices H with a confining potential NV where V is analytic and uniformly convex. From work by Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit of the…

We established and estimate the full asymptotic expansion in integer powers of 1 N of the [ $\sqrt$ N ] first marginals of N-body evolutions lying in a general paradigm containing Kac models and non-relativistic quantum evolution. We prove…

In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on…