We show that there is a unique Markov trace on the tower of Temperley– Lieb type quotients of Hecke algebras of Coxeter type E n (for all n ≥ 6). We explain in detail how this trace may be computed easily using tom Dieck's calculus of diagrams. As applications, we show how to use the trace to show that the diagram representation is faithful, and to compute leading coefficients of certain Kazhda...

Motivated by the problem of partisan gerrymandering, we introduce an electoral system for a representative democracy called democratic cellular voting designed to make modern packing and cracking strategies irrelevant by allowing districts to be influenced directly by voters through elections. We introduce an example of a democratic cellular voting system, called CV0, that is suitable for dynam...

In this paper we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. We show that, under the assumption that the conditional probability that our diffusion (Xs, s ≥ 0) doesn’t cross an upper boundary g(·) prior to time t given that Xt = z behaves as (a+ o(1))(g(t)− z) as z ↑ g(t), there exi...

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel me...

Abstract: We use the martingale method to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the way, we obtain bounds on certain martingale differences associated with the random sequences, which may be of independent interest. As an applicatio...

This paper presents a multiscale-based analysis of the statistical dependencies between the wavelet coefficients of random fields. In particular, in contrast to common decorrelated-coefficient models, we find that the correlation between wavelet scales can be surprisingly substantial, even across several scales. In this paper we investigate eight possible choices of statistical-interaction mode...

We study occupation time on hypersurface for Markov n-dimensional jump processes. Solvability and uniqueness of integro-differential Kolmogorov-Fokker-Planck with generalized functions in coefficients are investigated. Then these results are used to show that the occupation time on hypersurfaces does exist for the jump processes as a limit in variance for a wide class of piecewise smooth hypers...

Owing to their theoretical and practical significance, (1) has received great attention and has been recently studied extensively, andwe heremention Skorokhod [1] andMao and Yuan [2] among many others. However, in the real world, the condition that coefficients f and g in (1) are perturbed by the same Markovian chain is too restrictive. For example, in the classical Black-Scholes model, the ass...

The problem of consistent estimation of the regression coefficients when some prior information about the regression coefficients is available is considered. Such prior information is expressed in the form of exact linear restrictions. The knowledge of covariance matrix of measurement errors that is associated with explanatory variables is used to construct the consistent estimators. Some consi...

This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficien...