相关论文: Second-order Markov random fields for independent …
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D…
For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we…
Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…
We discuss the existence and characterization of quasi-stationary distributions and Yaglom limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean the existence of a deterministic function $g$ and a…
We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
There has recently been much interest in Gaussian fields on linear networks and, more generally, on compact metric graphs. One proposed strategy for defining such fields on a metric graph $\Gamma$ is through a covariance function that is…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
The Dirichlet forms related to various infinite systems of interacting Brownian motions are studied. For a given random point field $ \mu $, there exist two natural infinite-volume Dirichlet forms $…
We consider the random wetting transition on the Cayley tree, i.e. the problem of a directed polymer on the Cayley tree in the presence of random energies along the left-most bonds. In the pure case, there exists a first-order transition…
We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-spin systems at the critical threshold of…
We study random surfaces with a uniformly convex gradient interaction in the presence of quenched disorder taking the form of a random independent external field. Previous work on the model has focused on proving existence and uniqueness of…
In this paper, we study the Hard Core (HC) model with a countable set $\mathbb Z$ of spin values on a Cayley tree of order $k=2$. This model is defined by a countable set of parameters (that is, the activity function $\lambda_i>0$, $i\in…
The theory of Markov processes on the square lattice has been given recently by the second author a new algebraic description in terms of operads. In particular, this new approach allows for a nice description of invariant boundary…
Markov random fields are known to be fully characterized by properties of their information diagrams, or I-diagrams. In particular, for Markov random fields, regions in the I-diagram corresponding to disconnected vertex sets in the graph…
We discuss numerically the non-perturbative effects in exponential random graphs which are analogue of eigenvalue instantons in matrix models. The phase structure of exponential random graphs with chemical potential for 4-cycles and degree…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for the model. Using a contour argument we show the existence…
We derive two sufficient conditions for a function of a Markov random field (MRF) on a given graph to be a MRF on the same graph. The first condition is information-theoretic and parallels a recent information-theoretic characterization of…
The hard-core model has attracted much attention across several disciplines, representing lattice gases in statistical physics and independent sets in discrete mathematics and computer science. On finite graphs, we are given a parameter…