Fixation for Distributed Clustering Processes (2009)
Hilario, Marcelo R., Louidor, Oren, Newman, Charles M., Rolla, Leonardo T., Sheffield, Scott, Sidoravicius, Vladas
We study a discrete-time resource flow in $Z^d$, where wealthier vertices attract the resources of their less rich neighbors. For any translation-invariant probability distribution of initial...
Ising (Conformal) Fields and Cluster Area Measures (2008)
Camia, Federico, Newman, Charles M.
We provide a representation for the scaling limit of the d=2 critical Ising magnetization field as a (conformal) random field using SLE (Schramm-Loewner Evolution) clusters and associated...
SLE(6) and CLE(6) from Critical Percolation (2006)
Camia, Federico, Newman, Charles M.
We review some of the recent progress on the scaling limit of two-dimensional critical percolation; in particular, the convergence of the exploration path to chordal SLE(6) and the "full" scaling...
Two-Dimensional Critical Percolation: The Full Scaling Limit (2006)
Camia, Federico, Newman, Charles M.
We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the...
Critical Percolation Exploration Path and SLE(6): a Proof of Convergence (2006)
Camia, Federico, Newman, Charles M.
It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE(6). We provide here a detailed...
The Full Brownian Web as Scaling Limit of Stochastic Flows (2005)
Fontes, Luiz Renato, Newman, Charles M.
In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all space-time trajectories of a class of one-dimensional stochastic flows converges...
The Full Scaling Limit of Two-Dimensional Critical Percolation (2005)
Camia, Federico, Newman, Charles M.
We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the...
Convergence of Coalescing Nonsimple Random Walks to The Brownian Web (2005)
Newman, Charles M; Courant Institute Of Mathematical Sciences, New York University, New York, NY 10; Newman@cims.nyu.edu, Ravishankar, Krishnamurthi; SUNY-New Paltz, New Paltz, NY 12561, USA; Ravishak@newpaltz.edu, Sun, Rongfeng; EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlanda; Rsun@euridice.tue.nl
Abstract The Brownian Web (BW) is a family of coalescing Brownian motions starting from every point in space and time $RtimesR$. It was first introduced by Arratia, and later analyzed in detail by...
Continuum Nonsimple Loops and 2D Critical Percolation (2003)
Camia, Federico, Newman, Charles M.
Substantial progress has been made in recent years on the 2D critical percolation scaling limit and its conformal invariance properties. In particular, chordal SLE6 (the Stochastic Loewner Evolution...
The Percolation Transition in the Zero-Temperature Domany Model (2003)
Camia, Federico, Newman, Charles M.
We analyze a deterministic cellular automaton $\sigma^{\cdot} = (\sigma^n : n \geq 0)$ corresponding to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice...
A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models (2003)
Camia, Federico, Newman, Charles M., Sidoravicius, Vladas
We study families of dependent site percolation models on the triangular lattice ${\mathbb T}$ and hexagonal lattice ${\mathbb H}$ that arise by applying certain cellular automata to independent...
Clusters and recurrence in the two-dimensional zero-temperature stochastic ising model (2002)
Camia, Federico, De Santis, Emilio, Newman, Charles M.
We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of $+1$ or $-1$ to...
Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems (2002)
De Santis, Emilio, Newman, Charles M.
We consider stochastic processes, S^t \equiv (S_x^t : x \in Z^d), with each S_x^t taking values in some fixed finite set, in which spin flips (i.e., changes of S_x^t) do not raise the energy. We...
Cardy's Formula for some Dependent Percolation Models (2001)
Camia, Federico, Newman, Charles M., Sidoravicius, Vladas
We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular...
Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice (2001)
Camia, Federico, Newman, Charles M., Sidoravicius, Vladas
We investigate zero-temperature dynamics on the hexagonal lattice H for the homogeneous ferromagnetic Ising model with zero external magnetic field and a disordered ferromagnetic Ising model with a...
Special Invited Paper: Geodesics And Spanning Tees For Euclidean FirstPassage Percolaton (2001)
Howard, C. Douglas, Newman, Charles M.
The metric $D_{\alpha}(q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $\mathbb{R}^d$ , defined as the infimum of (\sum_i |q_i - q_{i+1}|^{\alpha})^{1/\alpha}$ over...
Probabilistic Analysis of Neural Networks. (1998)
Faris, William G., Newman, Charles M.
The research was a probabilistics study of neural network models. It was not oriented toward the workings of a particular device, but was intended to provide an understanding of the basic mechanisms...
Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions (1998)
Aizenman, Michael, Burchard, Almut, Newman, Charles M., Wilson, David B.
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a...
Percolation and contact processes with low-dimensional inhomogeneity (1997)
Newman, Charles M., Wu, C. Chris
We consider inhomogeneous nearest neighbor Bernoulli bond percolation on $mathbb{Z}^d$ where the bonds in a fixed $s$-dimensional hyperplane $1\leq s\leq d-1)$ have density $p_1$ and all other bonds...
Thermodynamic Chaos And The Structure Of Short-Range Spin Glasses (1997)
Charles M. Newman, Daniel L. Stein
This paper presents an approach, recently introduced by the authors and based on the notion of \metastates", to the chaotic size dependence expected in systems with many competing pure states,...
Geodesics in two-dimensional first-passage percolation (1996)
Licea, Cristina, Newman, Charles M.
We consider standard first-passage percolation on $\mathbb{Z}^2$. Geodesics are nearest-neighbor paths in $\mathbb{Z}^2$, each of whose segments is time-minimizing. We prove part of the conjecture...
Persistent survival of one-dimensional contact processes in random environments (1996)
Newman, Charles M., Volchan, Sergio B.
Consider an inhomogeneous contact process on Z 1 in which the recovery rates $\delta(x)$ at site x are i.i.d. random variables (bounded above) while the infection rate is a constant $\varepsilon$....
Disordered Ising systems and random cluster representations (1994)
Abstract. We discuss the Fortuin–Kasteleyn (FK) random cluster representation for Ising models with no external field and with pair interactions which need not be ferromagnetic. In the...
Ultralocal quantum field theory in terms of currents. (1971)
Thesis (Ph. D.)--Princeton.
Convergence of the sum of reciprocal renewal times
Necessary and sufficient conditions are given for the almost sure convergence or divergence of [summation operator][infinity]n=1(T1+ ... + Tn)-1, where T1, T2,... are i.i.d. and positive.
Ising (conformal) fields and cluster area measures
Camia, Federico, Newman, Charles M.
We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) random field by using Schramm–Loewner Evolution clusters and associated...