Related papers: Brownian Loops and the Selberg Zeta Function

We study the product of Selberg Zeta function and hyperbolic Eisenstein series on a family of degenerating hyperbolic surfaces.

We study branching Brownian motion in hyperbolic space. As hyperbolic Brownian motion is transient, the normalised empirical measure of branching Brownian motion converges to a random measure $\mu_\infty$ on the boundary. We show that the…

We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces $\mathbb{CP}^n$ and $\mathbb{CH}^n$. The characteristic functions of those processes are computed and limit theorems are…

Given a compact orientable surface of negative Euler characteristic, there exists a natural pairing between the Teichmueuller space of the surface and the set of homotopy classes of simple loops and arcs. The length pairing sends a…

For nonsupersymmetric theories, the one-loop effective action can be computed via zeta function regularization in terms of the functional trace of the heat kernel associated with the operator which appears in the quadratic part of the…

We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.

We introduce a framework to study the random entire function $\zeta_\beta$ whose zeros are given by the Sine$_\beta$ process, the bulk limit of beta ensembles. We present several equivalent characterizations, including an explicit power…

Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite random quadrangulation of this surface with $n$ faces and boundary component lengths of order $\sqrt n$ or of lower order. Endow this…

In this note we introduce and solve a soft classification version of the famous Bayesian sequential testing problem for a Brownian motion's drift. We establish that the value function is the unique non-trivial solution to a free boundary…

The Lie group Sol(p,q) is the semidirect product induced by the action of the real numbers R on the plane R^2 which is given by (x,y) --> (exp{p z} x, exp{-q z} y), where z is in R. Viewing Sol(p,q) as a 3-dimensional manifold, it carries a…

We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an…

Brownian motion in confinement and at interfaces is a canonical situation, encountered from fundamental biophysics to nanoscale engineering. Using the Lorenz-Mie framework, we optically record the thermally-induced tridimensional…

A Brownian loop is a random walk circuit of infinitely many, suitably infinitesimal, steps. In a plane such a loop may or may not enclose a marked point, the origin, say. If it does so it may wind arbitrarily many times, positive or…

We study the random metric space called the Brownian plane, which is closely related to the Brownian map and is conjectured to be the universal scaling limit of many discrete random lattices such as the uniform infinite planar…

We show that, under certain natural assumptions, large random plane bipartite maps with a boundary converge after rescaling to a one-parameter family ($\mathrm{BD}_L$, $0 < L < \infty$) of random metric spaces homeomorphic to the closed…

We simulate several models of random curves in the half plane and numerically compute their stochastic driving process (as given by the Loewner equation). Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE)…

We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These…

We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way…

Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow and thus Ornstein theory yielded the existence of a measure-preserving isomorphism…

We consider a family of free multiplicative Brownian motions $b_{s,\tau}$ parametrized by a real variance parameter $s$ and a complex covariance parameter $\tau.$ We compute the Brown measure $\mu_{s,\tau}$ of $ub_{s,\tau },$ where $u$ is a…