Related papers: Tightness for the interfaces of one-dimensional vo…
We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
The goal of this work is to find the asymptotics of the hitting probability of a distant point for the voter model on the integer lattice started from a single 1 at the origin. In dimensions 2 or 3, we obtain the precise asymptotic behavior…
Repeated sampling is a standard way to spend test-time compute, but its benefit is controlled by the latent distribution of correctness across examples, not by one-call accuracy alone. We study the binary correctness layer of repeated LLM…
For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…
We theoretically study subgap states appearing at the interface between two three-dimensional topological insulators which have different configurations in the spin-orbit interactions from each other. The coupling of spin…
We introduce an epistemic information measure between two data streams, that we term $influence$. Closely related to transfer entropy, the measure must be estimated by epistemic agents with finite memory resources via sampling accessible…
Let $P \subset \mathbb{R}^{2}$ be a Katz-Tao $(\delta,s)$-set, and let $\mathcal{L}$ be a Katz-Tao $(\delta,t)$-set of lines in $\mathbb{R}^{2}$. A recent result of Fu and Ren gives a sharp upper bound for the $\delta$-covering number of…
We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard…
Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
A method for studying exact properties of a class of {\it inhomogeneous} stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a ``zealot'', an individual allowed to favour an…
We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We…
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
Plurality and approval voting are two well-known voting systems with different strengths and weaknesses. In this paper we consider a new voting system we call beta(k) which allows voters to select a single first-choice candidate and approve…
By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, \textit{et al.} Phys. Rev. Lett. \textbf{87}, 045701 (2001)], we show that they behave differently from…
We examine a weighted-network multi-agent model with preferential selection such that agents choose partners with the probability $p(w)$, where $w$ is the number of their past selections. When $p(w)$ increases sublinearly with the number of…
We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase…
There exist a number of results proving that for certain classes of interacting particle systems in population genetics, mutual invadability of types implies coexistence. In this paper we prove a sort of converse statement for a class of…
For the model of two-dimensional random interlacements in the critical regime (i.e., $\alpha=1$), we prove that the vacant set is a.s.\ infinite, thus solving an open problem from arXiv:1502.03470. Also, we prove that the entrance measure…