Discrete low-discrepancy sequences (2009)
Angel, Omer, Holroyd, Alexander E., Martin, James B., Propp, James
Holroyd and Propp used Hall's marriage theorem to show that, given a probability distribution pi on a finite set S, there exists an infinite sequence s_1,s_2,... in S such that for all integers k >=...
Batch queues, reversibility and first-passage percolation (2009)
We consider a model of queues in discrete time, with batch services and arrivals. The case where arrival and service batches both have Bernoulli distributions corresponds to a discrete-time M/M/1...
Fragmenting random permutations (2008)
Goldschmidt, Christina; Department Of Statistics, University Of Oxford; Goldschm@stats.ox.ac.uk, Martin, James B; Department Of Statistics, University Of Oxford; Martin@stats.ox.ac.uk, Spano, Dario; Department Of Statistics, University Of Warwick; D.Spano@warwick.ac.uk
Problem 1.5.7 from Pitman's Saint-Flour lecture notes: Does there exist for each n a fragmentation process (Πn,k, 1 ≤ k ≤ n) such that Πn,k is distributed like the partition generated by...
Concentration results for a Brownian directed (2008)
B. M. Hambly, James B. Martin, Neil O'connell
percolation problem.
Collision probabilities in the rarefaction fan of asymmetric exclusion processes (2008)
Ferrari, Pablo A., Goncalves, Patricia, Martin, James B.
We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate $p\in(1/2,1]$ and to the left at rate $1-p$, interacting by exclusion. In the...
Fragmenting random permutations (2007)
Goldschmidt, Christina, Martin, James B., Spanò, Dario
Problem 1.5.7 from Pitman's Saint-Flour lecture notes: Does there exist for each n a fragmentation process (\Pi_{n,k}, 1 \leq k \leq n) taking values in the space of partitions of {1,2,...,n} such...
Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues (2007)
Ferrari, Pablo A., Martin, James B.
In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x$ whose nearest neighbor to the right is at y, jumps...
A phase transition for competition interfaces (2007)
Ferrari, Pablo A., Martin, James B., Pimentel, Leandro P. R.
We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this...
Coagulation–fragmentation duality, Poisson–Dirichlet distributions and random recursive trees (2006)
Dong, Rui, Goldschmidt, Christina, Martin, James B.
In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose...
Heavy tails in last-passage percolation (2006)
We consider last-passage percolation models in two dimensions, in which the underlying weight distribution has a heavy tail of index alpha
Multiclass processes, dual points and M/M/1 queues (2005)
Ferrari, Pablo A., Martin, James B.
We consider the discrete Hammersley-Aldous-Diaconis process (HAD) and the totally asymmetric simple exclusion process (TASEP) in Z. The basic coupling induces a multiclass process which is useful in...
The Jammed Phase of the Biham-Middleton-Levine Traffic Model (2005)
Angel, Omer; University Of British Columbia, Canada; Angel@math.ubc.ca, Holroyd, Alexander E.; University Of British Columbia, Canada; Holroyd@math.ubc.ca, Martin, James B.; CNRS And Université Paris 7, France; James.Martin@liafa.jussieu.fr
Initially a car is placed with probability $p$ at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive...
Dong, Rui, Goldschmidt, Christina, Martin, James B.
In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose...
Random Recursive Trees and the Bolthausen-Sznitman Coalesent (2005)
Goldschmidt, Christina; Statistical Laboratory And Pembroke College, University Of Cambridge, UK; C.Goldschmidt@statslab.cam.ac.uk, Martin, James B.; CNRS And Université Paris 7, France; James.Martin@liafa.jussieu.fr
We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the...
The Jammed Phase of the Biham-Middleton-Levine Traffic Model (2005)
Angel, Omer, Holroyd, Alexander E, Martin, James B
Initially a car is placed with probability p at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent...
Random recursive trees and the Bolthausen-Sznitman coalescent (2005)
Goldschmidt, Christina, Martin, James B.
We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the...
Stationary distributions of multi-type totally asymmetric exclusion processes (2005)
Ferrari, Pablo A., Martin, James B.
We consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\mathbb {Z}$ and on the cycle $\mathbb {Z}_N$. Angel recently gave an elegant...
Roughening and inclination of competition interfaces (2004)
Ferrari, Pablo A., Martin, James B., Pimentel, Leandro P. R.
The competition interface between two growing ``Young clusters'' (diagrams), in a two-dimensional random cone, is mapped to the path of a second-class particle in the one-dimensional totally...
A universality property for last-passage percolation paths close to the axis (2004)
Bodineau, Thierry, Martin, James B.
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the...
Limiting shape for directed percolation models (2004)
We consider directed first-passage and last-passage percolation on the nonnegative lattice ℤ+d, d≥2, with i.i.d. weights at the vertices. Under certain moment conditions on the common...
Ellen K. Pedersen, Theresa L. Bedford, William E. Grant, S. Bradleigh Vinson, James B. Martin, Michael T. Longnecker, ...
We examined effects of the exotic fire ant Solenopsis invicta on habitat use by hispid cotton rats (Sigmodon hispidus) and northern pygmy mice (Baiomys taylori) over a 17-month period in an open...
Reconstruction thresholds on regular trees (2003)
We consider a branching random walk with binary state space and index set $T^k$, the infinite rooted tree in which each node has k children (also known as the model of "broadcasting on a tree"). The...
Limiting shape for directed percolation models (2003)
We consider directed first-passage and last-passage percolation on the nonnegative lattice Z_+^d, d\geq2, with i.i.d. weights at the vertices. Under certain moment conditions on the common...
Reconstruction thresholds on regular trees (2003)
We consider the model of broadcasting on a tree, with binary state space, on the infinite rooted tree k in which each node has k children. The root of the tree takes a random value 0 or 1, and...
Pitman's 2M-X Theorem for Skip-Free Random Walks with Markovian Increments (2001)
Hambly, B. M.; University Of Oxford; Hambly@maths.ox.ac.uk, Martin, James B.; Cambridge University; Jbm11@cus.cam.ac.uk, O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr
Let $(xi_k, kge 0)$ be a Markov chain on ${-1,+1}$ with $xi_0=1$ and transition probabilities $P(xi_{k+1}=1| xi_k=1)=a>b=P(xi_{k+1}=-1| xi_k=-1)$. Set $X_0=0$, $X_n=xi_1+cdots +xi_n$ and...
Point processes in fast Jackson networks (2001)
We consider a Jackson-type network, each of whose nodes contains N identical channels with a single server. Upon arriving at a node, a task selects m of the channels at random and joins the shortest...
Large Tandem Queueing Networks with Blocking (2000)
Systems consisting of many queues in series have been considered by Glynn and Whitt (1991) and Baccelli, Borovkov and Mairesse (2000). We extend their results to apply to situations where the queues...
Linear Growth for Greedy Lattice Animals (2000)
Let $d\geq 2$, and let ${X_\bv, \bv\in\ZZ^d$ be an i.i.d.\ family of non-negative random variables with common distribution $F$. Let $N(n)$ be the maximum value of $\sum_\bv\in\xiX_\bv$ over all...
Point Processes in Fast Jackson Networks (2000)
We consider a Jackson-type network, each of whose nodes contains $N$ identical channels with a single server. Upon arriving at a node, a task selects $m$ of the channels at random, and joins the...
Large Tandem Queueing Networks with Blocking (2000)
Systems consisting of many queues in series have been considered by Glynn and Whitt (1991) and Baccelli, Borovkov and Mairesse (2000). We extend their results to apply to situations where the queues...
Linear Growth for Greedy Lattice Animals (2000)
Let $d\geq 2$, and let ${X_\bv, \bv\in\ZZ^d$ be an i.i.d.\ family of non-negative random variables with common distribution $F$. Let $N(n)$ be the maximum value of $\sum_\bv\in\xiX_\bv$ over all...
Point Processes in Fast Jackson Networks (2000)
We consider a Jackson-type network, each of whose nodes contains $N$ identical channels with a single server. Upon arriving at a node, a task selects $m$ of the channels at random, and joins the...
Large Tandem Queueing Networks with Blocking (2000)
Systems consisting of many queues in series have been considered by Glynn and Whitt (1991) and Baccelli, Borovkov and Mairesse (2000). We extend their results to apply to situations where the queues...
Linear Growth for Greedy Lattice Animals (2000)
Let $d\geq 2$, and let ${X_\bv, \bv\in\ZZ^d$ be an i.i.d.\ family of non-negative random variables with common distribution $F$. Let $N(n)$ be the maximum value of $\sum_\bv\in\xiX_\bv$ over all...
Point Processes in Fast Jackson Networks (2000)
We consider a Jackson-type network, each of whose nodes contains $N$ identical channels with a single server. Upon arriving at a node, a task selects $m$ of the channels at random, and joins the...
Thesis (B.S.)--California Polytechnic State University, 1992.
Evaluation of healthcare software from a usability perspective (1990)
Lowery, Julie C., Martin, James B.
This paper provides a framework for evaluating healthcare software from a usability perspective. The framework is based on a review of both the healthcare software literature and the general...
Evaluation of an advance surgical scheduling system (1989)
Martin, James B., Lowery, Julie C.
Utilization of the surgical suite is of significant concern to administrators because of the high costs associated with this facility. Scheduling systems, which control the flow of patients into the...
Friedman, Bruce A., Martin, James B.
Physicians are commonly being excluded from meaningful participation in the planning, implementation, and operation of automated medical systems in hospitals. The authors advocate a rapid shift...
An integarted surgical suite management information system (1984)
Martin, James B., Cantrell, Mary E., Fichman, Robert G., Hunsberger, Phillip K., Radoyevich, Myra
The operational aspects, application areas, and results achieved from an integrated surgical suite management information system are described. The system, which has been operating within Henry Ford...