Results 1  10
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60
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 439 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
A p* primer: logit models for social networks
 SOCIAL NETWORKS
, 1999
"... A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others wHolland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions ..."
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Cited by 57 (0 self)
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A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others wHolland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, pp. 33–65 Ž with discussion.; Fienberg, S.E., Wasserman,
On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted
, 1997
"... This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic setup provided by a Markov structure that suggests natural coupling variables. More specifically ..."
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Cited by 32 (1 self)
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This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic setup provided by a Markov structure that suggests natural coupling variables. More specifically, given a stationary Markov chain X�t � , and a function U = U�X�t��, we propose a way to study the proximity of U to a normal random variable when the state space is large. We apply the general method to the study of two problems. In the first, we consider the antivoter chain X�t � =�X �t� i �i∈ � � t = 0 � 1���� � where � is the vertex set of an nvertex regular graph, and X �t� i =+1or−1. The chain evolves from time t to t + 1 by choosing a random vertex i, and a random neighbor of it j, and setting X �t+1� i =−X �t� j and X�t+1� k = X �t� k for all k = i. For a stationary antivoter chain, we study the normal approximation of Un = U �t� n = ∑ i X �t� i for large n and consider some conditions on sequences of graphs such that Un is asymptotically normal, a problem posed by Aldous and Fill. The same approach may also be applied in situations where a Markov chain does not appear in the original statement of a problem but is constructed as an auxiliary device. This is illustrated by considering weighted Ustatistics. In particular we are able to unify and generalize some results on normal convergence for degenerate weighted Ustatistics and provide rates. 1. Introduction and
Hydrodynamic Scaling, Convex Duality, and Asymptotic Shapes of Growth Models
, 1996
"... . We present a technique for simultaneously deriving two related results: Hydrodynamic scaling limits for onedimensional asymmetric particle systems and asymptotic shapes for growth models. The idea is to specify the particle dynamics in terms of a microscopic LaxOleinik formula which leads direct ..."
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Cited by 23 (4 self)
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. We present a technique for simultaneously deriving two related results: Hydrodynamic scaling limits for onedimensional asymmetric particle systems and asymptotic shapes for growth models. The idea is to specify the particle dynamics in terms of a microscopic LaxOleinik formula which leads directly to the macroscopic description in terms of a nonlinear conservation law. The law of large numbers required for this link comes from the growth model that is embedded in the particle system. In the limit, the asymptotic shape of the growth model becomes the convex conjugate of the flux of the conservation law, and the latter is computable from the particle system in equilibrium. The asymptotic shape is then obtained from the duality relation. The method is illustrated with four applications. Mathematics Subject Classification: Primary 60K35, Secondary 60C05, 82C22 Keywords: Hydrodynamic scaling limit, growth model, LaxOleinik formula, convex duality Address: Department of Mathematics, Iow...
SuperBrownian Limits of Voter Model Clusters
 Ann. Probab. 29, 1001–1032 (2001) Zbl pre01906008 MR 2003c:60160
, 2000
"... this paper, we will study the limiting spatial structure of the voter model in d ..."
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Cited by 13 (4 self)
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this paper, we will study the limiting spatial structure of the voter model in d
Improved Lower Bound On The Thermodynamic Pressure Of The Spin 1/2 Heisenberg Ferromagnet
"... . We introduce a new stochastic representation of the partition function of the spin 1/2 Heisenberg ferromagnet. We express some of the relevant thermodynamic quantities in terms of expectations of functionals of so called random stirrings on Z d . By use of this representation we improve the lowe ..."
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Cited by 13 (0 self)
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. We introduce a new stochastic representation of the partition function of the spin 1/2 Heisenberg ferromagnet. We express some of the relevant thermodynamic quantities in terms of expectations of functionals of so called random stirrings on Z d . By use of this representation we improve the lower bound on the pressure given by Conlon and Solovej in [CS2]. AMS subject classification (1991): 82D40, 82B20 1. Introduction and Result We consider the 1 2 spin isotropic quantum Heisenberg ferromagnet (QHF) on the ddimensional hypercubic lattice. The Hamiltonian of the model is H = 1 2 X jx\Gammayj=1 h (S(x) \Gamma S(y)) 2 \Gamma 1 i (1.1) where S(x) = (S X (x); S Y (x); S Z (x)) ; x 2 , are the local spin operators and the summation runs over nearest neighbour pairs of lattice sites in the rectangular box , with periodic boundary conditions. The canonical commutation relations satisfied by the spin operators are: \Theta S ff (x); S fi (y) = iffi x;y ffl ff;fi;fl S fl ...
The Dynamics of Defect Ensembles in OneDimensional Cellular Automata
, 1994
"... We investigate the dynamics of ensembles of diffusive defects in onedimensional deterministic cellular automata. The work builds on earlier results on individual random walks in c.a. (5;6) . Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. ..."
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Cited by 11 (3 self)
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We investigate the dynamics of ensembles of diffusive defects in onedimensional deterministic cellular automata. The work builds on earlier results on individual random walks in c.a. (5;6) . Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties becomes transparent from this analysis. Keywords: Cellular automaton, permutivity, topological defect, random walk. AMS Classification: 58F08, 60K35, 82C41 1 Research partially supported by the Academy of Finland and The Finnish Cultural Foundation 1 Introduction Topological defects, Bloch walls or contours can be identified in a number of standard lattice model...
Ergodicity for spin systems with stirrings
 Ann. Probab
, 1990
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 10 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Microscopic Selection Principle for a DiffusionReaction Equation
 Journal of Statistical Physics
, 1986
"... We consider a model of stochastically interacting particles on 2~, where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate 7/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmo ..."
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Cited by 9 (2 self)
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We consider a model of stochastically interacting particles on 2~, where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate 7/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V(7,) then satisfies 7 ~/2V(Y) ~ ~/2 as y. oo. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor},~/2 and letting y ~ oo. This density solves the reactiondiffusion equation u, = 89 + u(1u), and under Heaviside initial data converges to a traveling wave moving at the same rate,fi. KEY WORDS: Diffusionreaction equation.
Can Stable Social Groups be Maintained by Homophilous Imitation Alone
 Journal of Economic Behavior and Organization
, 2005
"... A central problem in the biological and social sciences concerns the conditions required for emergence and maintenance of cooperation among unrelated individuals. Most models and experiments have been pursued in a gametheoretic context and involve reward or punishment. Here we show that such payoff ..."
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Cited by 6 (0 self)
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A central problem in the biological and social sciences concerns the conditions required for emergence and maintenance of cooperation among unrelated individuals. Most models and experiments have been pursued in a gametheoretic context and involve reward or punishment. Here we show that such payoffs are unnecessary, and that stable social groups can sometimes be maintained provided simply that agents are more likely to imitate others who are like them (homophily). In contrast to other studies, to sustain multiple types we need not impose the restriction that agents also choose to make their opinions different from those in other groups.