Related papers: The Non-Orientable Map Asymptotics Constant $p_g$

Asymptotic couplings by reflection are constructed for a class of non-linear monotone SPDES (stochastic partial differential equations). As applications, the gradient/H\"older estimates as well as the exponential convergence are derived for…

A pair of linearly independent asymptotic solutions are constructed for the second-order linear difference equation {equation*} P_{n+1}(x)-(A_{n}x+B_{n})P_{n}(x)+P_{n-1}(x)=0, {equation*} where $A_n$ and $B_n$ have asymptotic expansions of…

We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the…

In this manuscript, we establish asymptotic local exponential stability of the trivial solution of differential equations driven by H\"older--continuous paths with H\"older exponent greater than $1/2$. This applies in particular to…

We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…

The general framework on the non-local Markovian symmetric forms on weighted $l^p$ $(p \in [1, \infty])$ spaces constructed by [A,Kagawa,Yahagi,Y 2020], by restricting the situation where $p =2$, is applied to such measure spaces as the…

This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…

We prove some asymptotic results for the radius and the profile of large random bipartite planar maps. Using a bijection due to Bouttier, Di Francesco and Guitter between rooted bipartite planar maps and certain two-type trees with positive…

We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for…

Let $\Gamma_{g}$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We develop a new method for integrating over the representation space $\mathbb{X}_{g,n}=\mathrm{Hom}(\Gamma_{g},S_{n})$ where $S_{n}$ is…

Let $X_\lambda^\mu := X_\lambda \cap X^\mu \subseteq G/P$ be a Richardson variety in a generalized partial flag manifold. We use equivariant stable map spaces to define a canonical resolution $\widetilde{X_\lambda^\mu}$ of singularities,…

We consider non-orientable closed surfaces of minimum crosscap number in the $(p,q)$-lens space $L(p,q) \cong V_1 \cup_{\partial} V_2$, where $V_1$ and $V_2$ are solid tori. Bredon and Wood gave a formula for calculating the minimum…

We study an ergodic problem associated to a non-local Hamilton-Jacobi equation defined on the whole space $\lambda-\mathcal{L}[u](x)+|Du(x)|^m=f(x)$ and determine whether (unbounded) solutions exist or not. We prove that there is a…

This work is concerned with the iterative regularization of a non-smooth nonlinear ill-posed problem where the forward mapping is merely directionally but not G\^ateaux differentiable. Using a Bouligand subderivative of the forward mapping,…

Given an undirected graph $G$, let us randomly orient $G$ by tossing independent (possibly biased) coins, one for each edge of $G$. Writing $a\rightarrow b$ for the event that there exists a directed path from a vertex $a$ to a vertex $b$…

In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…

Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…

It has been shown by various authors under different assumptions that the diameter of a bounded non-trivial set $\gamma$ under the action of a stochastic flow grows linearly in time. We show that the asymptotic linear expansion speed if…

Given two one-dimensional families $f$ and $g$ of regular plane polynomial automorphisms parameterised by an algebraic curve $B$, all defined over some number field $K$, such that one of them is dissipative, we prove that at any parameter…

A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random…