Poisson limit of bumping routes in the Robinson–Schensted correspondence

We consider the Robinson–Schensted–Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the y-axis) when a specified number is inserted into a large Plancherel-distributed random tableau. We show that after a projective change of the coordinate system the bumping route converges in distribution to the Poisson process.

PROJECTIVE CHANGE BETWEEN RANDERS METRIC AND EXPONENTIAL (A, B)-METRIC

In this paper, we find the conditions to characterize projective change between two (A, B)-metrics, such as exponential (A, B)-metric, and Randers metric L=A+B on a manifold with dim n > 2, where A and A are two Riemannian metrics, B and B are two non-zero 1-forms. Further, we discussed the special curvature properties of two classes of (A, B)-metrics.

β-Change of Riemannian Space and Special Cases of one-form β

In this paper, we consider β-change of Finsler metric L given by L = f(L; β), where f is any positively homogeneous function of degree one in L and β. The objectives of the paper are to obtain the β-change of a Riemannian space, projective change of Finsler metric and to discuss the special cases of one-form β.

Recurrent Finsler manifolds under projective change

The aim of the present paper is to provide an intrinsic investigation of some important special Finsler spaces. These spaces are related to the Berwald [Formula: see text]-curvature tensor of transformed manifold, the Douglas tensor and the projective deviation tensor of projective change. Three spaces are studied and called symmetric, [Formula: see text]-recurrent and [Formula: see text]-recurrent manifolds.