相关论文: Curvature of basis exchange walks
In this paper, we establish, for the first time, upper bounds of the Ricci--curvature for Riemannian submersions along the vertical distribution as well as along both the vertical and horizontal distributions. We derive their general forms…
We prove upper and lower bounds on the number of pairs of commuting $n\times n$ matrices with integer entries in $[-T,T]$, as $T\to \infty$. Our work uses Fourier analysis and leads us to an analysis of exponential sums involving matrices…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
The comparison of Receiver Operating Characteristic (ROC) curves is frequently used in the literature to compare the discriminatory capability of different classification procedures based on diagnostic variables. The performance of these…
A 3-dimensional graph-manifold is composed from simple blocks which are products of compact surfaces with boundary by the circle. Its global structure may be as complicated as one likes and is described by a graph which might be an…
We consider a random walk $\tilde S$ which has different increment distributions in positive and negative half-planes. In the upper half-plane the increments are mean-zero i.i.d. with finite variance. In the lower half-plane we consider two…
We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and…
In a previous article it was shown that when a three-dimensional smooth convex body has rotational symmetry around a coordinate axis one can find better bounds for the lattice point discrepancy than what is known for more general convex…
We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers' method. Finally, some examples arising from the…
A subvariety V of an abelian variety is `translate' if it is the union of translates of proper algebraic subgroups. An irreducible V is `transverse' if it is not contained in any translate variety. Effective sharp lower bounds for a…
We give upper and lower bounds on the largest singular value of a matrix using analogues to walks in graphs. For nonnegative matrices these bounds are asymptotically tight. In particular, we improve a bound due to I. Schur.
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second…
Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…
In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition.…
We observe that there are elliptic curves over number fields all of whose quadratic twists must have positive rank, assuming the Birch-Swinnerton-Dyer conjecture. We give a classification of such curves in terms of their local behaviour,…
We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
For metric spaces with curvature less than or equal to x, x<0, it is shown that a recurrent geodesic can be approximated by closed geodesics. A counter example is provided for the converse.
We present the first rigorous quantitative analysis of once-reinforced random walks (ORRW) on general graphs, based on a novel change of measure formula.~This enables us to prove large deviations estimates for the range of the walk to have…
Due to their high cross field mobility, neutral atoms can have a strong effect on transport even at the low relative densities found inside the separatrix. We use a charge-exchange dominated model for the neutrals, coupled to neoclassical…