Related papers: A Guide to Stochastic Loewner Evolution and its Ap…
We suggest how to give a physical interpretation of Stochastic Loewner Evolution traces approaching a marked point in the upper half plane. We show that this may be related to the fusion of boundary with bulk fields in Conformal Field…
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
The fundamental lemma by Jan C. Willems and co-workers, which is deeply rooted in behavioral systems theory, has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style…
The Stochastic Series Expansion (SSE) technique is a quantum Monte Carlo method that is especially efficient for many quantum spin systems and boson models. It was the first generic method free from the discretization errors affecting…
We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We consider the Schramm-Loewner evolution (SLE$_\kappa$) with $\kappa=4$, the critical value of $\kappa > 0$ at or below which SLE$_\kappa$ is a simple curve and above which it is self-intersecting. We show that the range of an SLE$_4$…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We revisit the convergence of loop-erased random walk, LERW, to SLE(2) when the curves are parametrized by capacity. We construct a coupling of the chordal version of LERW and chordal SLE(2) based on the Green's function for LERW as…
This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their…
We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD). Building on the recent work of Ben Arous, Gheissari, and Jagannath on the effective dynamics of SGD, we study the critical scaling regime of…
The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…