Related papers: Unavoidable collections of balls for processes wit…

We classify measures on $\{0,1\}^{\mathbb{Z}^d}$, $d \geq 3$, the space of subsets of $\mathbb{Z}^d$, which are invariant under all affine special linear transformations. In other words, we classify simple point processes on $\mathbb{Z}^d$…

Given a countable group G, we consider the sets S_factor(G), S_eqrel(G), of subgroups F of the positive real line for which there exists a free ergodic probability measure preserving action G on X such that the fundamental group of the…

For an uncountable cardinal \tau and a subset S of an abelian group G, the following conditions are equivalent: (i) |{ns:s\in S}|\ge \tau for all integers n\ge 1; (ii) there exists a group homomorphism \pi:G\to T^{2^\tau} such that \pi(S)…

Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree $d$ polynomial with random multiplicative $\pm1$ coefficients is irreducible in $\mathbb{Z}[x]$ with probability…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

Let $\Gamma$ be a Zariski-dense subgroup of a reductive group $\mathbf{G}$ defined over a field $F$. Given a finite collection of finite subgroups $H_i$ ($i \in I$) of $\mathbf{G}(F)$ avoiding the center, we establish a criterion to ensure…

In this paper we study a family of nonlinear (conditional) expectations that can be understood as a semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a time and path-dependent…

We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) well-spread, and (iii) a certain random variable on the…

Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process…

We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…

We study the problem of when a Brownian motion in the unit ball has a positive probability of avoiding a countable collection of spherical obstacles. We give a necessary and sufficient integral condition for such a collection to be…

Let g be an integer greater than 1. A uniform version of the Parshin-Arakelov theorem on the finiteness of the set of non-isotrivial curves of genus g over a function field, with fixed degeneracy locus, is proved. This is applied to obtain…

We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1-block…

We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…

Graphons $W$ can be used as stochastic models to sample graphs $G_n$ on $n$ nodes for $n$ arbitrarily large. A graphon $W$ is said to have the $H$-property if $G_n$ admits a decomposition into disjoint cycles with probability one as $n$…

The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on groups. It is strict if and only if the random walk does not behave like the uniform measure on balls. We prove that, in any nonelementary…

The Grothendieck-Serre conjecture predicts that every generically trivial torsor under a reductive group $G$ over a regular semilocal ring $R$ is trivial. We establish this for unramified $R$ granted that $G^{\mathrm{ad}}$ is totally…

The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter $\alpha\in(0,2]$. This process has an infinitesimal generator…

Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may be modeled by a set M whose density inside X is…

We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak…