Related papers: Generic stability, randomizations, and NIP formula…

We consider the problem of solving TAP mean field equations by iteration for Ising model with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical…

Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near…

In this article we define generalized pairs $(X, B+\boldsymbol{\beta})$ where $X$ is an analytic variety and $\boldsymbol{\beta}$ is a b-(1,1) current. We then prove that almost all standard results of the MMP hold in this generality for…

Consider a sphere of radius root(n) in n dimensions, and consider X, a random variable uniformly distributed on its surface. Poincare's Observation states that for large n, the distribution of the first k coordinates of X is close in total…

Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a measurable space $(X,\cal X)$ with distribution $\mu$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $\mu_n$ denote the…

In this note we consider the stability of posterior measures occuring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function. This extends the well-posedness analysis of Bayesian inverse problems. In…

Kim's Lemma is a key ingredient in the theory of forking independence in simple theories. It asserts that if a formula divides, then it divides along every Morley sequence in type of the parameters. Variants of Kim's Lemma have formed the…

Given a dynamical system, a characteristic measure is a Borel probability measure invariant under all of its automorphisms. Frisch and Tamuz asked if every symbolic system supports such a measure. Motivated by this problem, we study the…

Let P -> M be a principal G-bundle. Using techniques from the loop representation of gauge theory, we construct well-defined substitutes for ``Lebesgue measure'' on the space A of connections on P and for ``Haar measure'' on the group Ga of…

This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…

In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…

Given a countable sofic group $\Gamma$, a finite alphabet $A$, a subshift $X \subseteq A^\Gamma$, and a potential $\phi: X \to \mathbb{R}$, we give sufficient conditions on $X$ and $\phi$ for expressing, in the uniqueness regime, the sofic…

Recall that a definable group is `definably amenable' if it admits a translation-invariant Keisler measure. We prove a combinatorial characterization of definable amenability for groups definable in NIP theories. More specifically, given a…

We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…

We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.

We formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point. We give some examples,…

On a compact K\"ahler manifold $(X,\omega)$, we study the strong continuity of solutions with prescribed singularities of complex Monge-Amp\`ere equations with integrable Lebesgue densities. Moreover, we give sufficient conditions for the…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of $\operatorname{SL}(2,\mathbb{R})$ on smooth manifolds. Our main technical result, from which the rest of the…

We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space $\Omega$ which does not assume that all measures of the model have the same null sets. This is given by a diffferentiable…