Related papers: Inverting the Ray-Knight identity on the line
We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to…
We consider a variant of self-repelling random walk on the integer lattice Z where the self-repellence is defined in terms of the local time on oriented edges. The long-time asymptotic scaling of this walk is surprisingly different from the…
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…
We consider the continuous time version of the `true' or `myopic' self-avoiding random walk with site repulsion in 1d. The Ray-Knight-type method which was applied to the discrete time and edge repulsion case, is applicable to this model…
We prove that the rescaled ``true'' self-avoiding walk $(n^{-2/3}X_{\lfloor nt \rfloor})_{t\in\mathbb{R}_+}$ converges weakly as $n$ goes to infinity to the ``true'' self-repelling motion constructed by T\'oth and Werner. The proof features…
We consider a $d$-dimensional SDE with an identity diffusion matrix and a drift vector being a vector function of bounded variation. We give a representation for the derivative of the solution with respect to the initial data.
Since human-labeled samples are free for the target set, unsupervised person re-identification (Re-ID) has attracted much attention in recent years, by additionally exploiting the source set. However, due to the differences on camera…
Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation. Prior work has explored self-correction at inference time or during post-training; however, such…
We consider the slow nonlinear diffusion equation subject to a constant absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, where an initially advancing (receding) interface gives way to…
Recent deep-learning-based approaches to single-image reflection removal have shown promising advances, primarily for two reasons: 1) the utilization of recognition-pretrained features as inputs, and 2) the design of dual-stream interaction…
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a…
Single-cell RNA-seq profiles are high-dimensional, sparse, and unordered, causing autoregressive generation to impose an artificial ordering bias and suffer from error accumulation. To address this, we propose scDiVa, a masked discrete…
We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, namely \[ \left( \frac{dX}{dt}\right) ^{\perp}=-\kappa_{ss}N.…
Face recognition models embed a face image into a low-dimensional identity vector containing abstract encodings of identity-specific facial features that allow individuals to be distinguished from one another. We tackle the challenging task…
We present REWIND (Real-Time Egocentric Whole-Body Motion Diffusion), a one-step diffusion model for real-time, high-fidelity human motion estimation from egocentric image inputs. While an existing method for egocentric whole-body (i.e.,…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong…
Personalized generative diffusion models, capable of synthesizing highly realistic images based on a few reference portraits, may pose substantial social, ethical, and legal risks via identity replication. Existing defense mechanisms rely…
Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the…
Semi-discrete Runge-Kutta schemes for nonlinear diffusion equations of parabolic type are analyzed. Conditions are determined under which the schemes dissipate the discrete entropy locally. The dissipation property is a consequence of the…