Related papers: Conditional expectations of random holomorphic fie…
We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme…
The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the…
Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of…
We discuss duality properties of critical Boltzmann planar maps such that the degree of a typical face is in the domain of attraction of a stable distribution with parameter $\alpha\in(1,2]$. We consider the critical Bernoulli bond…
Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation…
Let $n\geq 2$ and $r\in \{1, \cdots, n-1\}$ be integers, $M$ be a compact smooth K\''ahler manifold of complex dimension $n$, $E$ be a holomorphic vector bundle with complex rank $r$ and equipped with an hermitian metric $h_E$, and $L$ be…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using…
Off-diagonal upper bounds are established away from the diagonal for the Bergman kernels associated to high powers of holomorphic line bundles over compact complex manifolds, asymptotically as the power tends to infinity. The line bundle is…
When the structure deformation is dominated by the low-energy deformation mode, the structure hardens with the increase in the size (number of units) at small sizes. This anomalous behavior will eventually disappear with the decay length of…
In periodically sheared suspensions there is a dynamical phase transition characterized by a critical strain amplitude $\gamma_c$ between an absorbing state where particle trajectories are reversible and an active state where trajectories…
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be…
Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling…
We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged and planar plates as a function of the salt concentration and surface charge…
We extend known methods to establish upper bounds on the least character non-residues contingent on different zero-free regions within the critical strip, in particular on bounded rectangles within the critical strip along the $\sigma=1$…
We investigate the realizations of a random Gaussian field on a finite domain of ${\mathbb R}^d$ in the limit where a given linear functional of the field is large. We prove that if its variance is bounded, the field converges uniformly and…
We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual. Discrete holomorphy is defined by a straightforward…