Related papers: Fixation probability in Moran-like Processes on gr…
We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. Burdzy and Pal in their paper proposed a continuous version of graphical models --…
Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios the information of interest resides…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
This article provides a representation theorem for a set of Gaussian processes; this theorem allows to build Gaussian processes with arbitrary regularity and to write them as limit of random trigonometric series. We show via Karhunen-Love…
We study the effect of the mutant's degree on the fixation probability, extinction and fixation times, in the Moran process on Erd\"{o}s-R\'{e}nyi and Barab\'{a}si-Albert graphs. We performed stochastic simulations and use mean-field type…
The appeal of thermodynamics to problems outside physics is undeniable, as is the growing recognition of its apparent universality, yet in the absence of a rigorous formalism divorced from the peculiarities of molecular systems all attempts…
Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal the martingale structure for a general thermodynamic functional…
Contemporary work implies generative machine learning models are capable of learning the phase behavior in condensed matter systems such as the Ising model. In this Letter, we utilize a score-based modeling procedure called Thermodynamic…
Asymptotic fluctuation theorems are statements of a Gallavotti-Cohen symmetry in the rate function of either the time-averaged entropy production or heat dissipation of a process. Such theorems have been proved for various general classes…
We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion…
A temporal-theoretic formalism for understanding game theory is described where a strict ordering relation on a set of time points $T$ defines a game on $T$. Using this formalism, a proof of Zermelo's Theorem, which states that every finite…
Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and…
The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
We study evolutionary game dynamics in finite populations. We analyze an evolutionary process, which we call pairwise comparison, for which we adopt the ubiquitous Fermi distribution function from statistical mechanics. The inverse…
The glass transition plays a central role in nature as well as in industry, ranging from biological systems such as proteins and DNA to polymers and metals. Yet the fundamental understanding of the glass transition which is a prerequisite…
The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…
Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on…
A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Their fundamental result…