Extreme first-passage events are broadly relevant to biological, chemical, and physical processes in which the first successful arrival determines the outcome. Existing theories are confined to noninteracting searchers. Interacting extreme-statistics problems are notoriously difficult because correlations destroy probability factorization. We establish a general framework for interacting extreme search. A no-go theorem shows that broad classes of bounded interactions cannot beat the $1/\ln N$ extreme timescale of $N$ independent Brownian searchers, and complementary upper bounds prove that this scale is exact for broad classes of repulsive interactions. We then identify two sharp mechanisms beyond the logarithmic class and derive a unified interaction-driven acceleration limit. In particular, deterministic pairwise interaction can at most reduce the extreme search time to order $1/N$, while stochastic pairwise forcing attains $1/(N\ln N)$. Our results separate acceleration due to statistical redundancy from that generated by coherent many-body transport or amplified fluctuations, deepening our understanding of interacting stochastic systems.
In many soft-matter and biological systems, task completion relies on the cumulative arrival of multiple searchers rather than the speed of a single pioneer. The completion kinetics are therefore set not only by the first arrival, but by the full ordered sequence of first-passage times. Here, we determine how stochasti...
Ron Vatash, Eden Goldfarb, V. Rudyak et al.· 0 citations
Let $(\xi_t)_{t \geq 0}$ be a continuous-time Markov process taking values in a countable state space $E$. We consider $k$ copies of $\xi$ started from distinct positions, and write $X = (X_t)_{t \geq 0}$ for the resulting process of configurations in $E^k$. We compare two forms of interaction between the particles: th...
A unified short-time framework for extreme reachability of continuous-time random walks on networks is developed, showing that both the many-walker limit and the frequent-resetting limit are controlled by the short-time asymptotics of the first-passage time distribution, determined by the network's shortest-path struct...
Fei Ma, Xincheng Hu, Jinzhi Ouyang et al.· Proceedings of the 32nd ACM...· 0 citations
We investigate the persistence of most probable paths through the Onsager--Machlup functional for multidimensional stochastic differential equations driven by fractional Brownian motion with time-dependent diffusion coefficients and Hurst parameter $H\in(1/4,1)$. Under suitable structural and variational conditions, de...
Extreme events are widely studied within simple random walk frameworks, where their probability is determined by the network structure and stationary walker distribution. Here, we propose a recovery random walk (RRW) model in which extreme events temporally `freeze'the nodes where they occur for a fixed duration $\Delt...
Karan Singh, V. NarendranR, V. K. Chandrasekar et al.· 0 citations
Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic tra...
James Gulliford, Gareth O. Roberts, Michael F. Faulkner· 0 citations
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