Related papers: Central limit theorems for interacting innovation …
Innovation is the driving force of human progress. Recent urn models reproduce well the dynamics through which the discovery of a novelty may trigger further ones, in an expanding space of opportunities, but neglect the effects of social…
This paper deals with a new design methodology for stratified comparative experiments based on interacting reinforced urn systems. The key idea is to model the interaction between urns for borrowing information across strata and to use it…
We consider systems of interacting Generalized Friedman's Urns (GFUs) having irreducible mean replacement matrices. The interaction is modeled through the probability to sample the colors from each urn, that is defined as convex combination…
We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We…
The aim of this paper is to study the asymptotic behavior of strongly reinforced interacting urns with partial memory sharing. The reinforcement mechanism considered is as follows: draw at each step and for each urn a white or black ball…
We complete the study of the model introduced in [11]. It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number of sampled balls at each time-step is random. We identify the…
In this paper we develop a theory to describe innovation processes in a network of interacting units. We introduce a stochastic picture that allows for the clarification of the role of fluctuations for the survival of innovations in such a…
Urn models for innovation capture fundamental empirical laws shared by several real-world processes. The so-called urn model with triggering includes, as particular cases, the urn representation of the two-parameter Poisson-Dirichlet…
In this work, we introduce an extremely general model for a collection of innovation processes in order to model and analyze the interaction among them. We provide theoretical results, analytically proven, and we show how the proposed model…
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…
Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The Urn Model with…
We introduce and discuss a special type of feedback interacting urn model with deterministic interaction. This is a generalisation of the very well known Eggenberger and Polya (1923) urn model. In our model, balls are added to a particular…
Interacting urns with exponential reinforcement were introduced and studied in Launay (2011). As its parameter $\rho$ tends to $\iy$, this reinforcement mechanism converges to the "generalized" reinforcement, in which the probability of…
We consider a network of interacting agents and we model the process of choice on the adoption of a given innovative product by means of statistical-mechanics tools. The modelization allows us to focus on the effects of direct interactions…
We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…
Data extracted from social media platforms, such as Twitter, are both large in scale and complex in nature, since they contain both unstructured text, as well as structured data, such as time stamps and interactions between users. A key…
In this work we introduce a new type of urn model with infinite but countable many colors indexed by an appropriate infinite set. We mainly consider the indexing set of colors to be the $d$-dimensional integer lattice and consider balanced…
We propose a stochastic model of opinion exchange in networks. A finite set of agents is organized in a fixed network structure. There is a binary state of the world and each agent receives a private signal on the state. We model beliefs as…
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems…
We study an urn process containing red and blue balls and two different strategies to reinforce the urn. Namely, a generalized P\'olya-type strategy versus an i.i.d. one. At each step, one of the two reinforcement strategies is chosen by…