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- Steven D. Galbraith, Mark Holmes
- Discrete Applied Mathematics
- 2010

We consider a generalisation of the birthday problem that arises in the analysis of algorithms for certain variants of the discrete logarithm problem in groups. More precisely, we consider sampling coloured balls and placing them in urns, such that the distribution of assigning balls to urns depends on the colour of the ball. We determine the expected… (More)

- M. Sznaier, M. Holmes
- 2004

This paper addresses the problem of designing stabilizing controllers that minimize the 7-l ~ norm of a certain closed-loop transfer function while maintaining the C1 norm of a different transfer function below a prespecified level. This problem arises in the context of rejecting both stochastic as well as bounded persistent disturbances. Alternatively, in… (More)

- Mark J Holmes, Kihyun Choi, Satoshi Kako, Munetaka Arita, Yasuhiko Arakawa
- Nano letters
- 2014

We demonstrate triggered single photon emission at room temperature from a site-controlled III-nitride quantum dot embedded in a nanowire. Moreover, we reveal a remarkable temperature insensitivity of the single photon statistics, and a g((2))[0] value at 300 K of just 0.13. The combination of using high-quality, small, site-controlled quantum dots with a… (More)

We study the asymptotic behaviour of random walks in i.i.d. random environments on Z d. The environments need not be elliptic, so some steps may not be available to the random walker. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience, and in 2-dimensions the existence of a deterministic limiting… (More)

Goodness-of-fit tests are a fundamental element in the copula-based modeling of multivariate continuous distributions. Among the different procedures proposed in the literature, recent large scale simulations suggest that one of the most powerful tests is based on the empirical process comparing the empirical copula with a parametric estimate of the copula… (More)

- Mark Holmes
- 2008

We use the lace expansion to prove asymptotic formulae for the Fourier transforms of the r-point functions for a spread-out model of critically weighted lattice trees in Z d for d > 8. A lattice tree containing the origin defines a sequence of measures on Z d , and the statistical mechanics literature gives rise to a natural probability measure on the… (More)

We prove that the drift θ(d, β) for excited random walk in dimension d is monotone in the excitement parameter β ∈ [0, 1], when d ≥ 9.

We derive a perturbation expansion for general interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the true (weakly) self-avoiding walk and loop-erased random walk. We use the expansion to prove a law of large numbers and… (More)

- M J A Holmes
- 2011

The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential de¯ection formulation. The way in which the differential de¯ection is incorporated into the overall solution method for a point… (More)

We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are permitted to take large steps. We study the asymptotic behaviour of networks in the limit of widely separated network branch points, and prove Gaussian behaviour… (More)