Related papers: Cutoff in separation for compact harmonic manifold

We consider the conservative H\'enon family at the period-doubling bifurcation of its fixed point and demonstrate that the separatrices of the fixed saddle point nearing the bifurcation split exponentially: given that $\lambda_+$ is the…

We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial…

We consider the random walk on the hypercube which moves by picking an ordered pair $(i,j)$ of distinct coordinates uniformly at random and adding the bit at location $i$ to the bit at location $j$, modulo $2$. We show that this Markov…

We develop a spectral cut-off construction of real-time oscillatory integrals associated with non-autonomous Hamiltonian evolution equations. Let \(H_0\) be a positive self-adjoint reference operator on a Hilbert space \(\Hilb\), and let…

We extend the formalism based on perturbative QCD that was developed in our previous work, and compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. All the…

We prove a general theorem on cutoffs for symmetric exclusion and interchange processes on finite graphs $G_N=(V_N,E_N)$, under the assumption that either the graphs converge geometrically and spectrally to a compact metric measure space,…

The boundedness tests for the number of compact integral manifolds of autonomous ordinary differential systems, of autonomous total differential systems, of linear systems of partial differential equations, of Pfaff systems of equations,…

Hamiltonian trajectories are strictly time-reversible. Any time series of Hamiltonian coordinates {q} satisfying Hamilton's motion equations will likewise satisfy them when played "backwards", with the corresponding momenta changing signs :…

We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean $\mathbf{R}^{n}$ for $n\geq8$. The metric perturbation may have arbitrarily…

We establish new instances of the cutoff phenomenon for geodesic paths and for the Brownian motion on compact hyperbolic manifolds. We prove that for any fixed compact hyperbolic manifold, the geodesic path started on a spatially localized…

Motivated by a recent paper of Gabai on the Whitehead contractible 3-manifold, we investigate contractible manifolds $M^n$ which decompose or split as $M^n = A \cup_C B$ where $A,B,C \approx \mathbb{R}^n$ or $A,B,C \approx \mathbb{B}^n$. Of…

The cutoff phenomenon describes a sharp transition in the convergence of a family of ergodic finite Markov chains to equilibrium. Many natural families of chains are believed to exhibit cutoff, and yet establishing this fact is often…

In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at $\frac{3}{4}…

Let (S(t)) be a one-parameter family S = (S(t)) of positive integral operators on a locally compact space L. For a possibly non-uniform partition of [0,1] define a measure on the path space C([0,1],L) by using a) S(dt) for the transition…

Random walk on the irreducible representations of the symmetric and general linear groups is studied. A separation distance cutoff is proved and the exact separation distance asymptotics are determined. A key tool is a method for writing…

We establish cutoff for a natural random walk (RW) on the set of perfect matchings (PMs). An $n$-PM is a pairing of $2n$ objects. The $k$-PM RW selects $k$ pairs uniformly at random, disassociates the corresponding $2k$ objects, then…

In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In…

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

Charmonium dissociation cross sections due to flavor-exchange charmonium-baryon scattering are computed in the constituent quark model. We present results for inelastic $J/\psi N$ and $\eta_c N$ scattering amplitudes and cross sections into…

This is a proof of an asymptotic formula which describes exponentially small splitting of separatrices in a generic analytic family of area-preserving maps near a Hamiltonian saddle-centre bifurcation. As a particular case and in…