We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …

``Self-Organised Criticality''(SOC) is the mechanism by which complex systems
spontaneously settle close to a* critical point*, at the edge between stability and chaos, and …

We consider the generalized Lotka–Volterra system of equations with all-to-all, random
asymmetric interactions describing high-dimensional, very diverse and well-mixed …

As a schematic model of the complexity economic agents are confronted with, we introduce
the “Sherrington-Kirkpatrick game,” a discrete time binary choice model inspired from mean …

We study the dynamics of the generalized Lotka-Volterra model with a network structure.
Performing a high connectivity expansion for graphs, we write down a mean-field dynamical …

We review the main methods used to study spin glasses. In the first part, we focus on
methods for fully connected models and systems defined on a tree, such as the replica …

This paper questions the dynamic stability of supplier-buyer networks. We investigate a
simple rewiring process, by which firms change suppliers if it increases profit, within an …

How do interactions between species influence their spatial distribution in an ecosystem? To
answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka …

Classical economics has developed an arsenal of methods, based on the idea of
representative agents, to come up with precise numbers for next year's GDP, inflation and …

A phase transition in high-dimensional random geometry is analyzed as it arises in a variety
of problems. A prominent example is the feasibility of a minimax problem that represents the …