Related papers: Cutoff in separation for compact harmonic manifold
One approach to produce a pair of homeomorphic-but-not-diffeomophic closed 4-manifolds is to find a knot which is smoothly slice in one but not the other. This approach has never been run successfully. We give the first examples of a pair…
Motivated by the study of the convex hull of the trajectory of a Brownian motion in the unit disk reflected orthogonally at its boundary, we study inhomogeneous fragmentation processes in which particles of mass $m \in (0,1)$ split at a…
In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that…
We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree…
We provide a new geometric representation of a family of fragmentation processes by nested laminations, which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation obtained by cutting a…
In this work, we only use data on the unstable manifold to locate the partition boundaries by checking folding points at different levels, which practically coincide with homoclinic tangencies (HTs). The method is then applied to the…
In this work, we prove the following three rigidity results: (i) in a real-analytic globally hyperbolic spacetime $(M,g)$ without boundary, the time separation function restricted to a thin exterior layer of a unknown compact subset $K…
The sequence of the simple random walks on Hamming schemes $\{H(n, q)\}_{n=1}^{\infty}$ has a cutoff phenomenon for each integer $q$ greater than or equal to $3$. In this paper, for the sequence of simple random walks on Hamming schemes…
The paper establishes the property of splittability of billiard boundary sequences in n dimensional cube into subsequences of fractional parts. This reveals a new property of integrable and weak perturbated Hamilton systems: under a simple…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
We study the distribution of the exit place of iterated Brownian motion in a cone, obtaining information about the chance of the exit place having large magnitude. Along the way, we determine the joint distribution of the exit time and exit…
Let p:N->M be a surjective map of smooth manifolds. We are concerned with singular perturbation problems associated to a pair of second order positive definite differential operators with no zero order terms, that are intertwined by p. We…
In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not generically exist in the dissipative framework. The theoretical…
We say that a linear space is harmonious if it is resolvable and admits an automorphism group acting sharply transitively on the points and transitively on the parallel classes. Generalizing old results by the first author et al. we present…
For any twisted ideal polygon in $\mathbb{H}^3$, we construct a harmonic map from $\mathbb{C}$ to $\mathbb{H}^3$ with a polynomial Hopf differential, that is asymptotic to the given polygon, and is a bounded distance from a pleated plane.…
In this study, we construct an analog of the Brownian motion on free unitary quantum groups and compute its cutoff profile.
We prove that for any two closed Riemannian manifolds $M^{2m}$ ($m\geq 1$) and $N$, there exists a minimizing (extrinsic) $m$-polyharmonic map for every free homotopy class in $[M^{2m}, N]$, provided that the homotopy group $\pi_{2m}(N)$ is…
We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white…
We construct families of pairs of Heegaard splittings that must be stabilized several times to become equivalent. The first such pair differs only by their orientation. These are genus n splittings of a closed 3-manifold that must be…
It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the…