Related papers: Asymptotics of dynamic ASEP using duality
This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…
We use a method, inspired by Pohozeav's work, to study asymptotic behaviors of non-variational elliptic systems in dimension n greater than two. The results apply to changing sign solutions.
We introduce the asymptotic spectrum of graphs and apply the theory of asymptotic spectra of Strassen (J. Reine Angew. Math. 1988) to obtain a new dual characterisation of the Shannon capacity of graphs. Elements in the asymptotic spectrum…
Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
We study a new process, which we call ASEP$(q,j)$, where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by $q\in (0,1)$ and where at most $2j\in\mathbb{N}$ particles per site are allowed. The…
The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…
We prove a duality between the asymmetric simple exclusion process (ASEP) with non-conservative open boundary conditions and an asymmetric exclusion process with particle-dependent hopping rates and conservative reflecting boundaries. This…
The asymptotic behavior of expanding, generic, $T^2$-Symmetric, vacuum spacetimes is examined via numerical simulations. After validation of the numerical methods, the properties of these generic spacetimes are explored and compared to…
We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We…
We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…
We consider a totally asymmetric simple exclusion on $\mathbb{Z}$ with the step initial condition, under the additional restriction that the first particle cannot cross a deterministally moving wall. We prove that such a wall may induce…
We study the asymptotic behaviour of a real-valued diffusion whose non-regular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge a.s. to one another at an…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
In this paper we study asymptotic distributions associated to piecewise quasi-polynomials. The main result obtained here is used in another paper of the authors "The equivariant index of twisted Dirac operators and semi-classical limits".
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…
We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of…
We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…
We prove asymptotic formulas for the complex coefficients of $(\zeta q;q)_\infty^{-1}$, where $\zeta$ is a root of unity, and apply our results to determine secondary terms in the asymptotics for $p(a,b,n)$, the number of integer partitions…
Using the generalized method of steepest descents for the case of two coalescing saddle points, we derive an asymptotic expression for the bivariate generating function of Dyck paths, weighted according to their length and their area in the…