相关论文: The noisy veto-voter model: a Recursive Distributi…

We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with…

Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…

We provide a new characterisation of Duquesne and Le Gall's $\alpha$-stable tree, $\alpha\in(1,2]$, as the solution of a recursive distribution equation (RDE) of the form $\mathcal{T}\overset{d}{=}g(\xi,\mathcal{T}_i, i\geq0)$, where $g$ is…

We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic…

We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically…

This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential…

We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for…

In elections, the vote shares or turnout rates show a strong spatial correlation. The logarithmic decay with distance suggests that a 2D noisy diffusive equation describes the system. Based on the study of U.S. presidential elections data,…

This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of…

Consider $n$ players whose "scores" are independent and identically distributed values $\{X_i\}_{i=1}^n$ from some discrete distribution $F$. We pay special attention to the cases where (i) $F$ is geometric with parameter $p\to0$ and (ii)…

The symmetric exclusion process and the voter model are two interacting particle systems for which a dual finite particle system allows one to characterize its invariant measures. Adding spontaneous births and deaths to the two processes…

We present a new theoretical perspective of data noising in recurrent neural network language models (Xie et al., 2017). We show that each variant of data noising is an instance of Bayesian recurrent neural networks with a particular…

In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X =^d…

Progress in theoretical physics is often made by the investigation of toy models, the model organisms of physics, which provide benchmarks for new methodologies. For complex systems, one such model is the adaptive voter model. Despite its…

We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…

The discrete unitary (reversible) analogues of the continuous (irreversible) tent maps are numerically investigated, in particular, the lengths probability distribution of their periodic orbits. It is found that its density can be well…

We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be flat, we seek for…

We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…

We give a comprehensive mean-field analysis of the Partisan Voter Model (PVM) and report analytical results for exit probabilities, fixation times, and the quasi-stationary distribution. In addition, and similarly to the noisy voter model,…

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when…