We study two variants of the notion of holes formed by planar simple random walk of time duration 2n and the areas associated with them. We prove in both cases that the number of holes of area greater than A(n), where {A(n)} is an increasing sequence, is, up to a logarithmic correction term, asymptotic to n · A(n) for a range of large holes, thus confirming an observation by Mandelbrot. A conse...

Abstract We study models of continuous-time, symmetric, Zd -valued random walks in random environment, driven by a field of i.i.d. random nearest-neighbor conductances ωx y ∈ [0,1] with a power law with an exponent γ near 0. We are interested in estimating the quenched asymptotic behavior of the on-diagonal heat-kernel hωt (0, 0). We show that for γ > d 2 , the spectral dimension is standard, i...

Abstract A simplified higher dimensional Randall-Sundrum-like model in 6 dimensions is considered. It has been observed previously by Goldberger and Wise that in such a self-interacting scalar theory on the bulk with a conical singularity there is mixing of renormalization of 4d brane couplings with that of the bulk couplings. We study the influence of the running bulk couplings on the running ...

Consider a system with K parallel single-servers, each with its own waiting room. Upon arrival, a job is to be routed to the queue of one of the servers. Finding routing policy that minimizes the total workload in the system is a known difficult problem in general. Even if the optimal policy is identified, the policy would require the full queue length information at the arrival of each job; fo...

Several calculations of 2and 3-point correlation functions in the deformed theory are presented. The central charge in the LuninMaldacena gravity dual is shown to be independent of the deformation parameter. Calculations show that 2and 3-point functions of chiral primary operators have no radiative corrections to lowest order in the interactions. Correlators of the operator tr(Z1Z2), which has ...

Consider a random matrix whose variance profile is random. This random matrix is ergodic in one channel realization if, for each column and row, the empirical distribution of the squared magnitudes of elements therein converges to a nonrandom distribution. In this paper, noncrossing partition theory is employed to derive expressions for several asymptotic eigenvalue moments (AEM) related quanti...

We prove that no local diffeomorphism invariant two-dimensional theory of the metric and the dilaton without higher derivatives can describe the exact string black hole solution found a decade ago by Dijkgraaf, Verlinde and Verlinde. One of the key points in this proof is the concept of dilaton-shift invariance. We present and solve (classically) all dilaton-shift invariant theories of two-dime...

Recent years have witnessed a growing concern over the issue of safety culture within high-risk industries. The purpose of the present review is to summarize and integrate the numerous reports and studies that have been conducted to define and assesses safety culture, as well as the highly related concept of safety climate. Safety professionals have increasingly turned their attention to social...

A key requirement for safety-critical systems that use Commercial Off-TheShelf (COTS) components is that the COTS components do not compromise the reliability, safety and security of the overall system. Safety wrappers can be seen as a means to control the integration of the (often disparate in nature) components to ensure fault tolerance, quality of service and security. This paper discusses n...

We investigate the structure of the Longo-Rehren inclusion for a nite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic inclusion of A. Ocneanu. In particular, we obtain a precise description of the sectors associated with the Longo-Rehren inclusions in terms of half braidings, which do not necessarily satisfy the usual condition of...