[
{
"id": "/id/eprint/16116",
"eprint_id": 16116,
"rev_number": 38,
"documents": [
{
"id": "/id/document/139865",
"doc_id": 139865,
"rev_number": 3,
"files": [
{
"id": "/id/file/414904",
"fileid": 414904,
"datasetid": "document",
"objectid": 139865,
"filename": "Caltech_Final_Thesis_Submission.pdf",
"mime_type": "application/pdf",
"hash": "bf4e0733895286bf0f7a36baa7de0bac",
"hash_type": "MD5",
"filesize": 662277,
"mtime": "2023-06-14 10:46:24",
"url": "/16116/1/Caltech_Final_Thesis_Submission.pdf"
}
],
"eprint_id": 16116,
"pos": 1,
"placement": 1,
"mime_type": "application/pdf",
"format": "application/pdf",
"format_desc": "original thesis. updated thesis received 20230718",
"language": "en",
"security": "internal",
"license": "other",
"main": "Caltech_Final_Thesis_Submission.pdf",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"content": "final"
},
{
"id": "/id/document/139866",
"doc_id": 139866,
"rev_number": 3,
"files": [
{
"id": "/id/file/414906",
"fileid": 414906,
"datasetid": "document",
"objectid": 139866,
"filename": "Caltech Final Thesis Submission.zip",
"mime_type": "application/zip",
"hash": "cd1296c9134dbe60202372548bba174f",
"hash_type": "MD5",
"filesize": 249910,
"mtime": "2023-06-14 10:46:33",
"url": "/16116/2/Caltech Final Thesis Submission.zip"
}
],
"eprint_id": 16116,
"pos": 2,
"placement": 2,
"mime_type": "application/zip",
"format": "application/zip",
"format_desc": "original source files",
"language": "en",
"security": "internal",
"license": "other",
"main": "Caltech Final Thesis Submission.zip",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"content": "archival"
},
{
"id": "/id/document/139867",
"doc_id": 139867,
"rev_number": 1,
"files": [
{
"id": "/id/file/414909",
"fileid": 414909,
"datasetid": "document",
"objectid": 139867,
"filename": "indexcodes.txt",
"mime_type": "text/plain",
"hash": "f4c96bb953830be0f1a507ea1d48b7da",
"hash_type": "MD5",
"filesize": 12788,
"mtime": "2023-06-14 10:50:29",
"url": "/16116/3/indexcodes.txt"
}
],
"eprint_id": 16116,
"pos": 3,
"placement": 3,
"mime_type": "text/plain",
"format": "other",
"format_desc": "Generate index codes conversion from application/pdf to indexcodes",
"language": "en",
"security": "public",
"license": "other",
"main": "indexcodes.txt",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"relation": {
"items": [
{
"type": "http://eprints.org/relation/isVersionOf",
"uri": "/id/document/139865"
},
{
"type": "http://eprints.org/relation/isVolatileVersionOf",
"uri": "/id/document/139865"
},
{
"type": "http://eprints.org/relation/isIndexCodesVersionOf",
"uri": "/id/document/139865"
}
]
}
},
{
"id": "/id/document/139870",
"doc_id": 139870,
"rev_number": 4,
"files": [
{
"id": "/id/file/415015",
"fileid": 415015,
"datasetid": "document",
"objectid": 139870,
"filename": "Umans approval for Anand senior thesis 20230615.pdf",
"mime_type": "application/pdf",
"hash": "b790761b8894791d514479ab6ca894c0",
"hash_type": "MD5",
"filesize": 756051,
"mtime": "2023-06-15 22:11:10",
"url": "/16116/4/Umans approval for Anand senior thesis 20230615.pdf"
}
],
"eprint_id": 16116,
"pos": 4,
"placement": 3,
"mime_type": "application/pdf",
"format": "application/pdf",
"format_desc": "Umans approval for Anand senior thesis 20230615",
"language": "en",
"security": "internal",
"license": "other",
"main": "Umans approval for Anand senior thesis 20230615.pdf",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"content": "other"
},
{
"id": "/id/document/139871",
"doc_id": 139871,
"rev_number": 1,
"files": [
{
"id": "/id/file/415022",
"fileid": 415022,
"datasetid": "document",
"objectid": 139871,
"filename": "indexcodes.txt",
"mime_type": "text/plain",
"hash": "6df6deb89569dbaade0f81218ceab7ee",
"hash_type": "MD5",
"filesize": 577,
"mtime": "2023-06-15 22:21:32",
"url": "/16116/5/indexcodes.txt"
}
],
"eprint_id": 16116,
"pos": 5,
"placement": 5,
"mime_type": "text/plain",
"format": "other",
"format_desc": "Generate index codes conversion from application/pdf to indexcodes",
"language": "en",
"security": "internal",
"license": "other",
"main": "indexcodes.txt",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"relation": {
"items": [
{
"type": "http://eprints.org/relation/isVersionOf",
"uri": "/id/document/139870"
},
{
"type": "http://eprints.org/relation/isVolatileVersionOf",
"uri": "/id/document/139870"
},
{
"type": "http://eprints.org/relation/isIndexCodesVersionOf",
"uri": "/id/document/139870"
}
]
}
},
{
"id": "/id/document/139973",
"doc_id": 139973,
"rev_number": 4,
"files": [
{
"id": "/id/file/416112",
"fileid": 416112,
"datasetid": "document",
"objectid": 139973,
"filename": "Anand Caltech Final Thesis Submission2.zip",
"mime_type": "application/zip",
"hash": "67d9ac427f784601a9c014474d1816ff",
"hash_type": "MD5",
"filesize": 249930,
"mtime": "2023-07-18 16:44:17",
"url": "/16116/6/Anand Caltech Final Thesis Submission2.zip"
}
],
"eprint_id": 16116,
"pos": 6,
"placement": 1,
"mime_type": "application/zip",
"format": "application/zip",
"format_desc": "updated source files",
"language": "en",
"security": "internal",
"license": "other",
"main": "Anand Caltech Final Thesis Submission2.zip",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"content": "archival"
},
{
"id": "/id/document/139974",
"doc_id": 139974,
"rev_number": 2,
"files": [
{
"id": "/id/file/416116",
"fileid": 416116,
"datasetid": "document",
"objectid": 139974,
"filename": "AnandCaltech_Final_Thesis_Submission2.pdf",
"mime_type": "application/pdf",
"hash": "eca99cec29cbb0b3956f6cd2b22a1ad3",
"hash_type": "MD5",
"filesize": 680799,
"mtime": "2023-07-18 16:45:37",
"url": "/16116/7/AnandCaltech_Final_Thesis_Submission2.pdf"
}
],
"eprint_id": 16116,
"pos": 7,
"placement": 7,
"mime_type": "application/pdf",
"format": "application/pdf",
"language": "en",
"security": "public",
"license": "other",
"main": "AnandCaltech_Final_Thesis_Submission2.pdf",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"content": "final"
},
{
"id": "/id/document/139991",
"doc_id": 139991,
"rev_number": 1,
"files": [
{
"id": "/id/file/416215",
"fileid": 416215,
"datasetid": "document",
"objectid": 139991,
"filename": "indexcodes.txt",
"mime_type": "text/plain",
"hash": "da5c3b7258d909c01a425ee318f4a111",
"hash_type": "MD5",
"filesize": 12668,
"mtime": "2023-07-25 16:07:40",
"url": "/16116/8/indexcodes.txt"
}
],
"eprint_id": 16116,
"pos": 8,
"placement": 8,
"mime_type": "text/plain",
"format": "other",
"format_desc": "Generate index codes conversion from application/pdf to indexcodes",
"language": "en",
"security": "public",
"license": "other",
"main": "indexcodes.txt",
"media_duration": "0",
"media_aspect_ratio": "0",
"media_sample_start": "0",
"media_sample_stop": "0",
"relation": {
"items": [
{
"type": "http://eprints.org/relation/isVersionOf",
"uri": "/id/document/139974"
},
{
"type": "http://eprints.org/relation/isVolatileVersionOf",
"uri": "/id/document/139974"
},
{
"type": "http://eprints.org/relation/isIndexCodesVersionOf",
"uri": "/id/document/139974"
}
]
}
}
],
"eprint_status": "archive",
"userid": 12889,
"dir": "disk0/00/01/61/16",
"datestamp": "2023-06-15 22:13:03",
"lastmod": "2023-11-08 18:51:43",
"status_changed": "2023-06-15 22:13:03",
"type": "thesis",
"metadata_visibility": "show",
"creators": {
"items": [
{
"email": "emiletimothy@outlook.com",
"id": "Anand-Emile-Timothy",
"name": {
"family": "Anand",
"given": "Emile Timothy"
},
"orcid": "0000-0003-2893-9469",
"show_email": "YES"
}
]
},
"title": "Pseudorandomness of the Sticky Random Walk",
"ispublished": "unpub",
"full_text_status": "public",
"keywords": "pseudorandomness, expander random walks, sticky random walk, Krawtchouk functions",
"abstract": "We extend the pseudorandomness of random walks on expander graphs using the sticky random walk. Golowich and Vadhan recently showed that expander random walks can fool all symmetric functions in total variation distance (TVD) up to an O(\u03bb pp) error in total variation distance, where lambda is the second largest eigenvalue of the expander and p is the size of the arbitrary alphabet used to label the vertices. It has been conjectured that the dependency on the pp term is not tight.
\r\n\r\nIn this paper, we resolve the conjecture in the affirmative for a family of expanders. We present a generalization of Guruswami and Kumar's sticky random walk for which prior results predicts a TVD upper bound of O(\u03bb pp) using a Fourier analytic approach. For this family of graphs, we use a combinatorial approach involving the Krawtchouk functions to derive a strengthened TVD of O(\u03bb). Furthermore, we present equivalencies between instances of the generalized sticky random walk, and, using linear-algebraic techniques, show that the generalized sticky random walk is an infinite family of expanders.
",
"date": "2023",
"date_type": "degree",
"id_number": "CaltechTHESIS:06142023-102020321",
"refereed": "FALSE",
"official_url": "https://resolver.caltech.edu/CaltechTHESIS:06142023-102020321",
"rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.",
"collection": "CaltechTHESIS",
"reviewer": "Kathy Johnson",
"local_group": {
"items": [
"Caltech Theory"
]
},
"deposited_by": "Emile Anand",
"deposited_on": "2023-06-15 22:13:03",
"doi": "10.7907/ze1k-6v37",
"divisions": {
"items": [
"div_eng"
]
},
"institution": "California Institute of Technology",
"thesis_type": "senior_major",
"thesis_advisor": {
"items": [
{
"email": "umans@cms.caltech.edu",
"id": "Umans-C-M",
"name": {
"family": "Umans",
"given": "Christopher M."
},
"orcid": "0000-0003-2893-9469",
"role": "advisor"
}
]
},
"thesis_committee": {
"items": [
{
"name": {
"family": "None",
"given": "None"
}
}
]
},
"thesis_degree": "BS",
"thesis_degree_grantor": "California Institute of Technology",
"thesis_defense_date": "2023-06-11",
"review_status": "approved",
"option_major": {
"items": [
"compsci"
]
},
"copyright_statement": "Author's Rights Authorization: I hereby certify that, if appropriate, I have obtained a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted here is the same as that approved by my advisory committee.\n\nI hereby grant to California Institute of Technology or its agents the non-exclusive license to archive and make accessible, under the conditions specified under \"Thesis Availability\" in this submission, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation, or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.",
"pub_year": "2023",
"author_list": "Anand, Emile Timothy"
}
]