Non-self-averaging Lyapunov exponent in random conewise linear systems.

We consider a simple model for multidimensional conewise linear dynamics around cusplike equilibria. We assume that the local linear evolution is either v^{'}=Av or Bv (with A, B independently drawn from a rotationally invariant ensemble of symmetric N×N matrices) depending on the sign of the first component of v. We establish strong connections with the random diffusion persistence problem.

Hawkes processes with infinite mean intensity.

The stability condition for Hawkes processes and their nonlinear extensions usually relies on the condition that the mean intensity is a finite constant. It follows that the total endogeneity ratio needs to be strictly smaller than unity. In the present Letter we argue that it is possible to have a total endogeneity ratio greater than unity without rendering the process unstable.

Radical Complexity.

This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally-but perhaps most importantly-(v) "radical complexity" that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined.

Crisis propagation in a heterogeneous self-reflexive DSGE model.

We study a self-reflexive DSGE model with heterogeneous households, aimed at characterising the impact of economic recessions on the different strata of the society. Our framework allows to analyse the combined effect of income inequalities and confidence feedback mediated by heterogeneous social networks. By varying the parameters of the model, we find different crisis typologies: loss of confidence may propagate mostly within high income households, or mostly within low income households, with a rather sharp transition between the two.

Cultural diversity and wisdom of crowds are mutually beneficial and evolutionarily stable.

The ability to learn from others (social learning) is often deemed a cause of human species success. But if social learning is indeed more efficient (whether less costly or more accurate) than individual learning, it raises the question of why would anyone engage in individual information seeking, which is a necessary condition for social learning's efficacy. We propose an evolutionary model solving this paradox, provided agents (i) aim not only at information quality but also vie for audience and prestige, and (ii) do not only value accuracy but also reward originality-allowing them to alleviate herding effects.

Amorphous Order and Nonlinear Susceptibilities in Glassy Materials.

We review 15 years of theoretical and experimental work on the nonlinear response of glassy systems. We argue that an anomalous growth of the peak value of nonlinear susceptibilities is a signature of growing "amorphous order" in the system, with spin-glasses as a case in point. Experimental results on supercooled liquids are fully compatible with the random first-order transition (RFOT) prediction of compact "glassites" of increasing volume as temperature is decreased, or as the system ages.

V-, U-, L- or W-shaped economic recovery after Covid-19: Insights from an Agent Based Model.

We discuss the impact of a Covid-19-like shock on a simple model economy, described by the previously developed Mark-0 Agent-Based Model. We consider a mixed supply and demand shock, and show that depending on the shock parameters (amplitude and duration), our model economy can display V-shaped, U-shaped or W-shaped recoveries, and even an L-shaped output curve with permanent output loss. This is due to the economy getting trapped in a self-sustained "bad" state.

Generalization of the Marčenko-Pastur problem.

We study the spectrum of generalized Wishart matrices, defined as F=(XY^{⊤}+YX^{⊤})/2T, where X and Y are N×T matrices with zero mean, unit variance independent and identically distributed entries and such that E[X_{it}Y_{jt}]=cδ_{i,j}. The limit c=1 corresponds to the Marčenko-Pastur problem. For a general c, we show that the Stieltjes transform of F is the solution of a cubic equation.

By force of habit: Self-trapping in a dynamical utility landscape.

Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximization.

Confidence collapse in a multihousehold, self-reflexive DSGE model.

We investigate a multihousehold dynamic stochastic general equilibrium (DSGE) model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short-lived recessions; and alternation of high- and low-output states where a relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium.

May's instability in large economies.

Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. Relying on results from random matrix theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong, or when substitutability of their production inputs is reduced.

Crossover from Linear to Square-Root Market Impact.

Using a large database of 8 million institutional trades executed in the U.S. equity market, we establish a clear crossover between a linear market impact regime and a square-root regime as a function of the volume of the order.

Can the glass transition be explained without a growing static length scale?

It was recently discovered that SWAP, a Monte Carlo algorithm that involves the exchange of pairs of particles of differing diameters, can dramatically accelerate the equilibration of simulated supercooled liquids in regimes where the normal dynamics is glassy. This spectacular effect was subsequently interpreted as direct evidence against a static, cooperative explanation of the glass transition such as the one offered by the random first-order transition (RFOT) theory. We explain the speedup induced by SWAP within the framework of the RFOT theory.

Universal scaling and nonlinearity of aggregate price impact in financial markets.

How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different time scales. Here we reveal that price impact has a universal nonlinear shape for trades aggregated on any intraday scale.

Edge mode amplification in disordered elastic networks.

Understanding how mechanical systems can be designed to efficiently transport elastic information is important in a variety of fields, including in materials science and biology. Recently, it has been discovered that certain crystalline lattices present "topologically-protected" edge modes that can amplify elastic signals. Several observations suggest that edge modes are important in disordered systems as well, an effect not well understood presently.

Genuine localization transition in a long-range hopping model.

We introduce and study a banded random matrix model describing sparse, long-range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and a mapping to a long-range epidemics model, we establish the phase diagram of the model. A genuine localization transition, with well defined mobility edges, appears as the hopping rate decreases slower than ℓ^{-2}, where ℓ is the distance.

Spontaneous instabilities and stick-slip motion in a generalized Hébraud-Lequeux model.

We revisit the Hébraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.

Why Do Markets Crash? Bitcoin Data Offers Unprecedented Insights.

Crashes have fascinated and baffled many canny observers of financial markets. In the strict orthodoxy of the efficient market theory, crashes must be due to sudden changes of the fundamental valuation of assets. However, detailed empirical studies suggest that large price jumps cannot be explained by news and are the result of endogenous feedback loops.

Ground-state statistics of directed polymers with heavy-tailed disorder.

In this mostly numerical study, we reconsider the statistical properties of the ground state of a directed polymer in a d=1+1 "hilly" disorder landscape, i.e., when the quenched disorder has power-law tails.

Turbulent fracture surfaces: a footprint of damage percolation?

We show that a length scale ξ can be extracted from the spatial correlations of the "steep cliffs" that appear on a fracture surface. Above ξ, the slope amplitudes are uncorrelated and the fracture surface is monoaffine. Below ξ, long-range spatial correlations lead to a multifractal behavior of the surface, reminiscent of turbulent flows.

Endogenous crisis waves: stochastic model with synchronized collective behavior.

We propose a simple framework to understand commonly observed crisis waves in macroeconomic agent-based models, which is also relevant to a variety of other physical or biological situations where synchronization occurs. We compute exactly the phase diagram of the model and the location of the synchronization transition in parameter space. Many modifications and extensions can be studied, confirming that the synchronization transition is extremely robust against various sources of noise or imperfections.

Branching-ratio approximation for the self-exciting Hawkes process.

We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics that are readily obtained from empirical data. The method we propose greatly simplifies the estimation of the Hawkes branching ratio, recently proposed as a proxy for market endogeneity and formerly estimated using numerical likelihood maximization.

Critical dynamical heterogeneities close to continuous second-order glass transitions.

We analyze, using inhomogeneous mode-coupling theory, the critical scaling behavior of the dynamical susceptibility at a distance ε from continuous second-order glass transitions. We find that the dynamical correlation length ξ behaves generically as ε(-1/3) and that the upper critical dimension is equal to six. More surprisingly, we find that ξ grows with time as ln²t exactly at criticality.

Agent-based models for latent liquidity and concave price impact.

We revisit the "ɛ-intelligence" model of Tóth et al. [Phys. Rev.

Explore or exploit? A generic model and an exactly solvable case.

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case.