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Ising models on locally tree-like graphs
Ising model random sparse graphs cavity method Bethe measures belief propagation local weak convergence
2015/8/21
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the...
The weak limit of Ising models on locally tree-like graphs
Ising model the temperature the last beta sequence
2015/8/20
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising m...
FACTOR MODELS ON LOCALLY TREE-LIKE GRAPHS
Factor models random graphs belief propagation Bethe measures Potts model independent set Gibbs measures free energy density local weak convergence
2015/8/20
We consider homogeneous factor models on uniformly sparse graph sequences converg-ing locally to a (unimodular) random tree T, and study the existence of the free energy density ,the limit of the log...
This paper studies the formation of risk-sharing networks through costly social
investments, identifying endogenous inequality and a misallocation of resources as possible
downsides to such agreemen...
REMARKS ON OLDROYD-B AND RELATED COMPLEX FLUID MODELS
REMARKS ON OLDROYD-B RELATED COMPLEX FLUID MODELS
2014/4/3
We prove global existence and uniqueness of solutions of Oldroyd-B systems with relatively small data in Rd, in a large functional setting (Cα ∩ L1). This is a stability result,solutions select an equ...
Transition densities for stochastic Hodgkin-Huxley models
Hodgkin-Huxley model degenerate diffusion processes non time homogeneous diffusion processes Malliavin calculus Hormander condition
2012/7/11
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomog...
Moderate deviations for random field Curie-Weiss models
Random field Curie-Weiss model disordered mean-field moderate deviations large deviations transfer principle
2012/6/21
The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interes...
Max-stable models for multivariate extremes
Copula domain of attraction max-stable distribution spectral measure tail dependence
2012/4/17
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theo...
Exponential and non-exponential upper bounds for the ruin probabilities for the double Cox processes risk models
Probability Double Cox processes Martingale method
2011/11/4
In this paper, we consider a general insurance risk model in which the premium income process and the claim process are based on Cox processes. Exponential upper bounds for ruin probabilities are obta...
Distribution of branch lengths and phylogenetic diversity under homogeneous speciation models
phylogenetic tree birth–death process Yule model branch length
2011/9/23
Abstract: The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' whic...
Asymptotics of the Invariant Measure in Mean Field Models with Jumps
decoupling approximation fluid limit invariant measure McKean-Vlasov equation mean field limit small noise limit
2011/9/16
Abstract: We consider the asymptotics of the invariant measure for the process of the spatial distribution of $N$ coupled Markov chains in the limit of a large number of chains. Each chain reflects th...
Historical superprocess limits for population models with past dependence and competition
Historical superprocess interacting particle system limit theorem
2011/9/1
Abstract: We consider a population structured in trait. When a birth occurs, the trait of the parent is hereditarily transmitted to the offspring unless a mutation occurs. We associate with each indiv...
Asymptotic expansion of beta matrix models in the one-cut regime
Asymptotic expansion beta matrix models the one-cut regime Probability
2011/8/26
Abstract: We prove the existence of a 1/N expansion to all orders in beta matrix models with a confining, off-critical potential corresponding to an equilibrium measure with a connected support. Thus,...
Rotating states in driven clock- and XY-models
soft modes nonequilibrium dynamics Statistical Mechanics
2011/8/23
Abstract: We consider 3D active plane rotators, where the interaction between the spins is of XY-type and where each spin is driven to rotate. For the clock-model, when the spins take N\gg1 possible v...
Following [3], we consider the boundary WZW model on a half–plane with a cut growing according to the Schramm–Loewner stochastic evolution and the boundary fields inserted
at the tip of the cut and a...