Related papers: Extending P\'olya's random walker beyond probabili…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second…
Solving the exact renormalisation group equation a la Wilson-Polchinski perturbatively, we derive a power-counting theorem for general matrix models with arbitrarily non-local propagators. The power-counting degree is determined by two…
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.
Loop-weighted walk with parameter $\lambda\geq 0$ is a non-Markovian model of random walks that is related to the loop $O(N)$ model of statistical mechanics. A walk receives weight $\lambda^{k}$ if it contains $k$ loops; whether this is a…
Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~\cite{mgr, fmk,…
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…
We study the asymptotic behavior of the long cycles of a random permutation of $n$ objects with respect to multiplicative measures with polynomial growing cycle weights. We show that the longest cycle and the length differences between the…
The differential $\lambda$-calculus studies how the quantitative aspects of programs correspond to differentiation and to Taylor expansion inside models of linear logic. Recent work has generalized the axioms of Taylor expansion so they…
Let $X_{1,n}\le\cdots\le X_{n,n}$ be the order statistics of $n$ independent random variables with a common distribution function $F$ having right heavy tail with tail index $\gamma$. Given known constants $d_{i,n}$, $1\le i\le n$, consider…
Two-phase composites with non-overlapping inclusions randomly embedded in matrix are investigated. A straight forward approach is applied to estimate the effective properties of random 2D composites. First, deterministic boundary value…
We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated…
The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the…
We examine a random model consisting of objects with positive weights and evolving in discrete time steps, which generalizes certain random graph models. We prove almost sure convergence for the weight distribution and show scale-free…
A Plastic Quantum Walk admits both continuous time and continuous spacetime. The model has been recently proposed by one of the authors in \cite{molfetta2019quantum}, leading to a general quantum simulation scheme for simulating fermions in…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
In this paper we show how polynomial walks can be used to establish a twisted recurrence for sets of positive density in $\mathbb{Z}^d$. In particular, we prove that if $\Gamma \leq \operatorname{GL}_d(\mathbb{Z})$ is finitely generated by…
We dominate non-integral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators are minimal and our result applies to an array of situations, whose prototype are…