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Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative… (More)

- Julien Kockelkoren, Herbert Levine, Wouter-Jan Rappel
- Physical review. E, Statistical, nonlinear, and…
- 2003

We introduce a phase-field approach for diffusion inside and outside a closed cell with damping and with source terms at the stationary interface. The method is compared to exact solutions (where possible) and the more traditional finite element method. It is shown to be very accurate, easy to implement, and computationally inexpensive. We apply our method… (More)

- B. Tóth, J. Kockelkoren, J.-P. Bouchaud
- 2011

We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and vanishes around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are, to a first approximation, diffusive. This naturally accounts for two striking stylized… (More)

We argue that on electronic markets, limit and market orders should have equal effective costs on average. This symmetry implies a linear relation between the bid-ask spread and the average impact of market orders. Our empirical observations on different markets are consistent with this hypothesis. We then use this relation to justify a simple, and hitherto… (More)

We argue that on electronic markets, competition between liquidity providers should reduce the spread until the execution cost using market orders matches that of limit orders. This implies a linear relation between the bid-ask spread and the average impact of market orders, in good agreement with our empirical observations. We then use this relation to… (More)

- Julien Kockelkoren, Hugues Chaté
- Physical review letters
- 2003

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA-->(m+k)A, nA-->(n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of nontrivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair… (More)

- A Garèche, G Disdier, J Kockelkoren, J-P Bouchaud
- Physical review. E, Statistical, nonlinear, and…
- 2013

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation. Our description explicitly includes state dependence, i.e., the fact that the drift and diffusion depend on the volume present on both sides of the spread. "Jump" events, corresponding… (More)

Recent theoretical work has shown that so-called pulled fronts propagating into an unstable state always converge very slowly to their asymptotic speed and shape. In the light of these predictions, we reanalyze earlier experiments by Fineberg and Steinberg on front propagation in a Rayleigh–Bénard cell. In contrast to the original interpretation, we argue… (More)

The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lemâıtre & H. Chaté, Phys. Rev. Lett. 82, 1140 (1999)) are revisited with the help of detailed investigations of interface motion. It is shown that “normal”, curvature-driven-like domain growth is recovered at larger scales than considered before, and that the… (More)

We introduce a phase field approach for diffusion inside and outside a closed cell with damping and with source terms at the interface. The method is compared to exact solutions (where possible) and the more traditional finite element method. It is shown to be very accurate, easy to implement and computationally inexpensive. We apply our method to a… (More)