arXiv subjects

Yuki Chino

Publications and source records attributed to Yuki Chino.

6 recordsLinked to original sources

arXiv2026

An Explicit Representation of the Dominant Eigenstructure for Positive Operators on Banach Lattices

The Riesz projection and the corresponding eigenfunction of a positive operator satisfying the Doeblin condition are explicitly constructed using the partial Bell polynomials. While classical Fredholm theory requires stringent summability conditions, such as the operator being in a Schatten class to ensure the convergence of Fredholm minors, our approach utilizes the local algebraic structure induced by the Doeblin condition. We define a scalar function $D(λ)$ whose derivative $D'(λ_0)$ at the dominant eigenvalue $λ_0$ naturally provides the normalization constant for the projection. Consequently, an explicit functional representation of the eigenfunction is obtained as a limit of a weighted ratio of the operator's kernel, bypassing the need to solve transcendental characteristic equations.

math.FA↗

arXiv2026

Genealogical Expansions of Positive Fredholm Operators via a Reference-Point Method

We study positive Fredholm integral operators that arise as next-generation operators in structured population models. The main problem is to represent the dominant eigenvalue and the associated right and left eigenfunctions without using Fredholm determinants or finite-dimensional discretization. We introduce a reference-point construction: a rank-one correction on the space of kernels, determined by a fixed pair $(x_0,y_0)$, which reorganizes iterated kernels into a renewal-type series. Under an explicit dominant spectral separation assumption and a scalar non-resonance condition for the chosen reference pair, the resulting $\Gamma_n$-series converges at the spectral radius pointwise absolutely and gives the leading eigensystem. The coefficients also have a closed combinatorial expression in terms of ordinary partial Bell polynomials. For discrete-time integral projection models and for multi-state McKendrick equations, the same construction yields Euler--Lotka-type characteristic equations and formulas for demographic quantities such as stable distributions, reproductive values, type reproduction numbers, generation intervals, and expected generation numbers. The resulting genealogical expansion resolves the leading eigensystem into successive reproductive and transition contributions encoded by the iterated kernels.

q-bio.PE↗

arXiv2019

Random walk in cooling random environment: recurrence versus transience and mixed fluctuations

This is the third in a series of papers in which we consider one-dimensional Random Walk in Cooling Random Environment (RWCRE). The latter is obtained by starting from one-dimensional Random Walk in Random Environment (RWRE) and resampling the environment along a sequence of deterministic times, called refreshing times. In the present paper we explore two questions for general refreshing times. First, we investigate how the recurrence versus transience criterion known for RWRE changes for RWCRE. Second, we explore the fluctuations for RWCRE when RWRE is either recurrent or satisfies a classical central limit theorem. We show that the answer depends in a delicate way on the choice of the refreshing times. An overarching goal of our paper is to investigate how the behaviour of a random process with a rich correlation structure can be affected by resettings.

math.PR↗

arXiv2018

The random pinning model with correlated disorder given by a renewal set

We investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent $α$ > 0, when the correlated sequence is given by another independent renewal set with loop exponent $α$ > 0. Using the renewal structure of the disorder sequence, we compute the annealed critical point and exponent. Then, using a smoothing inequality for the quenched free energy and second moment estimates for the quenched partition function, combined with decoupling inequalities, we prove that in the case $α$ > 2 (summable correlations), disorder is irrelevant if $α$ < 1/2 and relevant if $α$ > 1/2, which extends the Harris criterion for independent disorder. The case $α$ $\in$ (1, 2) (non-summable correlations) remains largely open, but we are able to prove that disorder is relevant for $α$ > 1/ $α$, a condition that is expected to be non-optimal. Predictions on the criterion for disorder relevance in this case are discussed. Finally, the case $α$ $\in$ (0, 1) is somewhat special but treated for completeness: in this case, disorder has no effect on the quenched free energy, but the annealed model exhibits a phase transition.

math.PR↗

arXiv2016

Sharp transition in self-avoiding walk on random conductors on a tree

We consider self-avoiding walk on a tree with random conductances. It is proven that in the weak disorder regime, the quenched critical point is equal to the annealed one, and that in the strong disorder regime, these critical points are strictly different. Derrida and Spohn, and Baffet, Patrick and Pul$\acute{\rm e}$ give the exact value of the quenched critical point. We give another heuristic approach by the fractional moment estimate.

math.PR↗

arXiv2016

The quenched critical point for self-avoiding walk on random conductors

Following similar analysis to that in Lacoin (PTRF 159, 777-808, 2014), we can show that the quenched critical point for self-avoiding walk on random conductors on the d-dimensional integer lattice is almost surely a constant, which does not depend on the location of the reference point. We provide its upper and lower bounds that are valid for all dimensions.

math.PR↗