Related papers: Asymptotics for graphically divergent series: dens…

We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter $\epsilon$. We construct inner and outer solutions of the problem and relate them to asymptotic representations…

Using a recently developed method for proving asymptotics via orthogonal polynomial duality arXiv:2305.17602, we prove that the dynamic ASEP introduced in arXiv:1701.05239 has asymptotics which are either distributed as the Tracy--Widom…

In this paper we obtain precise asymptotics for certain families of graphs, namely circulant graphs and degenerating discrete tori. The asymptotics contain interesting constants from number theory among which some can be interpreted as…

Formulas for the expansion of arbitrary invariant group functions in terms of the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a combinatorial method. The method is similar to one used by Balantekin to expand…

Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the…

Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…

We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…

We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…

We present an asymptotic expansion for a family of multiple integrals connected with relatives of the Dickman function. The coefficients of this expansion have a similar arithmetic structure as those appearing in work of Soundararajan on an…

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…

Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to…

We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of…

For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length…

We consider the asymptotic expansion of the functional series \[S_{\mu,\gamma}(a;\lambda)=\sum_{n=1}^\infty \frac{n^\gamma e^{-\lambda n^2/a^2}}{(n^2+a^2)^\mu}\] for real values of the parameters $\gamma$, $\lambda>0$ and $\mu\geq0$ as…

We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\Gamma$ in ${\mathbb R}^p$, $p\geq2$, as $N \to \infty$. For $f$ decreasing…

Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is…

Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…