arXiv subjects

Pranay Agarwal

Publications and source records attributed to Pranay Agarwal.

7 recordsLinked to original sources

arXiv2025

Large Deviation Principle for Last Passage Percolation Models

Study of the KPZ universality class has seen the emergence of universal objects over the past decade which arise as the scaling limit of the member models. One such object is the directed landscape, and it is known that exactly solvable last passage percolation (LPP) models converge to the directed landscape under the KPZ scaling (see \cite{DV21}). Large deviations of the directed landscape on the metric level were recently studied in \cite{DDV24}, which also provides a general framework for establishing such large deviation principle (LDP). The main goal of the article is to apply and refine that framework to establish a LDP for LPP models at the metric level without relying on exact solvability. We then use the LDP on the metric level to establish a LDP for geodesics in these models, thus providing a streamlined way to study large transversal fluctuations of geodesics in these models. We briefly touch on how the theory extends to other planar models like directed polymers and Poisson LPP.

math.PR↗

arXiv2025

Content and Access Networks Synergies: Tradeoffs in Public and Private Investments by Content Providers

The ubiquity of smartphones has fueled content consumption worldwide, leading to an ever-increasing demand for a better Internet experience. This has necessitated an upgrade of the capacity of the access network. The Internet service providers (ISPs) have been demanding that the content providers (CPs) share the cost of upgrading access network infrastructure. A \emph{public investment} in the infrastructure of a neutral ISP will boost the profit of the CPs, and hence, seems a rational strategy. A CP can also make a \emph{private investment} in its infrastructure and boost its profits. In this paper, we study the trade-off between public and private investments by a CP when the decision is made under different types of interaction between them. Specifically, we consider four interaction models between CPs -- centralized allocation, cooperative game, non-cooperative game, and a bargaining game -- and determine the public and private investment for each model. Via numerical results, we evaluate the impact of different incentive structures on the utility of the CPs. We see that the bargaining game can result in higher public investment than the non-cooperative and centralized models. However, this benefit gets reduced if the CPs are incentivized to invest in private infrastructure.

cs.NI↗

arXiv2025

Improved universality bounds for directed polymers in the intermediate disorder regime

We prove universality of Tracy-Widom GUE fluctuations for directed polymers in $1+1$ dimensions in the intermediate disorder regime. Building on the Lindeberg replacement method of arXiv:2304.04871, we refine estimates for the measure of steep paths using probabilistic arguments. Our result extends the admissible range of the inverse temperature scaling parameter $β= n^{-α}$ to all $α\in (2/(3K+11), 1/4)$, provided the weights match $K$ moments with the log-Gamma distribution. For a general class of distributions, this gives universality for $α> 2/17$, and when the third moment vanishes, this threshold improves to $α> 1/10$. These results substantially broaden the known range of universality for directed polymers in the intermediate disorder regime.

math.PR↗

arXiv2025

Sharp deviation bounds for midpoint and endpoint of geodesics in exponential last passage percolation

For exponential last passage percolation on the plane we analyse the probability that the point-to-line geodesic exhibits an atypically large transversal fluctuation at the endpoint as well as the probability that the point-to-point geodesic exhibits an atypically large transversal fluctuation at the halfway point. In particular, we show that $p^*_n(t)$, the probability that the point-to-line geodesic from the origin to the line $x+y=2n$ ends at $(n-t(2n)^{2/3}, n+t(2n)^{2/3})$ satisfies that $n^{2/3}p^*_n(t)=\exp(-(\frac{4}{3}+o(1))t^{3})$ for $t$ large and $p_{n,\frac{1}{2}}(t)$, the probability that the geodesic from the origin to the point $(n,n)$ passes through the point $(\frac{1}{2}n-tn^{2/3}, \frac{1}{2} n+tn^{2/3})$, satisfies $n^{2/3}p_{n,\frac{1}{2}}(t)=\exp(-(\frac{8}{3}+o(1))t^3)$ for $t$ large. The latter result solves a special case of a conjecture from Liu (PTRF, 2022).

math.PR↗

arXiv2024

Content Provider Contributions to Capacity Expansion of a Neutral ISP: Effect of Private Option

Increasing content consumption by users and the expectation of a better Internet experience requires Internet service providers (ISPs) to expand the capacity of the access network continually. The ISPs have been demanding the participation of the content providers (CPs) in sharing the cost of upgrading the infrastructure. From CPs' perspective, investing in the ISP infrastructure, termed as \emph{public investment}, seems rational as it will boost their profit. However, the CPs can alternatively invest in making content delivery more efficient, termed as \emph{private investment}, as it also boosts their profit. Thus, in this work, we investigate this trade-off between public and private investment of the CPs for a net-neutral ISP. Specifically, we consider centralized decision and non-cooperative forms of interaction between CPs and an ISP and determine the optimum public and private investments of the CPs for each model. In the non-cooperative interaction, we find that at most one CP contributes to the public infrastructure, whereas all invest in their private infrastructure.

cs.NI↗

arXiv2023

Lower bound for large local transversal fluctuations of Geodesics in Last Passage Percolation

For exactly solvable models of planar last passage percolation, it is known that geodesics of length $n$ exhibit transversal fluctuations at scale $n^{2/3}$ and matching (up to exponents) upper and lower bounds for the tail probabilities are available. The local transversal fluctuations near the endpoints are expected to be much smaller; it is known that the transversal fluctuation up to distance $r \ll n$ is typically of the order $r^{2/3}$ and the probability that the fluctuation is larger than $tr^{2/3}$ is at most $Ce^{-ct^3}$. In this note, we provide a short argument establishing a matching lower bound for this probability.

math.PR↗

arXiv2023

Bayesian Variable Selection Under High-dimensional Settings With Grouped Covariates

Consider the normal linear regression setup when the number of covariates p is much larger than the sample size n, and the covariates form correlated groups. The response variable y is not related to an entire group of covariates in all or none basis, rather the sparsity assumption persists within and between groups. We extend the traditional g-prior setup to this framework. Variable selection consistency of the proposed method is shown under fairly general conditions, assuming the covariates to be random and allowing the true model to grow with both n and p. For the purpose of implementation of the proposed g-prior method to high-dimensional setup, we propose two procedures. First, a group screening procedure, termed as group SIS (GSIS), and secondly, a novel stochastic search variable selection algorithm, termed as group informed variable selection algorithm (GiVSA), which uses the known group structure efficiently to explore the model space without discarding any covariate based on an initial screening. Screening consistency of GSIS, and theoretical mixing time of GiVSA are studied using the canonical path ensemble approach of Yang et al. (2016). Performance of the proposed prior with implementation of GSIS as well as GiVSA are validated using various simulated examples and a real data related to residential buildings.

stat.ME↗